{"id":15273,"date":"2021-10-11T22:48:47","date_gmt":"2021-10-11T22:48:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/problem-set-9-graphs-of-linear-functions\/"},"modified":"2021-10-30T01:43:45","modified_gmt":"2021-10-30T01:43:45","slug":"problem-set-linear-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/problem-set-linear-functions\/","title":{"raw":"Problem Set: Linear Functions","rendered":"Problem Set: Linear Functions"},"content":{"raw":"For the following exercises, find the slope of the line that passes through the two given points.\r\n\r\n1. [latex]\\left(2,\\text{ }4\\right)[\/latex] and [latex]\\left(4,\\text{ 10}\\right)[\/latex]\r\n\r\n2.\u00a0[latex]\\left(1,\\text{ 5}\\right)[\/latex] and [latex]\\left(4,\\text{ 11}\\right)[\/latex]\r\n\r\n3. [latex]\\left(-1,\\text{4}\\right)[\/latex] and [latex]\\left(5,\\text{2}\\right)[\/latex]\r\n\r\n4. [latex]\\left(8,-2\\right)[\/latex] and [latex]\\left(4,6\\right)[\/latex]\r\n\r\n5. [latex]\\left(6,\\text{ }11\\right)[\/latex] and [latex]\\left(-4, 3\\right)[\/latex]\r\n\r\nFor the following exercises, find the slope of the lines graphed.\r\n\r\n6.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005131\/CNX_Precalc_Figure_02_01_201.jpg\" alt=\"\" \/>\r\n\r\n7.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005132\/CNX_Precalc_Figure_02_01_202.jpg\" alt=\"\" \/>\r\n\r\n8.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005132\/CNX_Precalc_Figure_02_01_203.jpg\" alt=\"\" \/>\r\n\r\nFor the following exercises, write an equation for the lines graphed.\r\n\r\n9.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005132\/CNX_Precalc_Figure_02_01_205.jpg\" alt=\"\" \/>\r\n\r\n10.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_206.jpg\" alt=\"\" \/>\r\n\r\n11.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_207.jpg\" alt=\"\" \/>\r\n\r\n12.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_208.jpg\" alt=\"\" \/>\r\n\r\n13.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_209.jpg\" alt=\"\" \/>\r\n\r\n14.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005134\/CNX_Precalc_Figure_02_01_210.jpg\" alt=\"\" \/>\r\n\r\nFor the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear equation that models the data.\r\n\r\n15.\r\n<table id=\"Table_02_01_04\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'g(x)'. Reading the remaining rows as ordered pairs (i.e., (x, g(x)), we have the following values: (0, 5), (5, -10), (10, -25), and (15, -40).\"><colgroup> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><strong><em>x<\/em><\/strong><\/td>\r\n<td>0<\/td>\r\n<td>5<\/td>\r\n<td>10<\/td>\r\n<td>15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>g<\/em>(<em>x<\/em>)<\/strong><\/td>\r\n<td>5<\/td>\r\n<td>\u201310<\/td>\r\n<td>\u201325<\/td>\r\n<td>\u201340<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n16.\r\n<table id=\"Table_02_01_05\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'h(x)'. Reading the remaining rows as ordered pairs (i.e., (x, h(x)), we have the following values: (0, 5), (5, 30), (10, 105), and (15, 230).\"><colgroup> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><strong><em>x<\/em><\/strong><\/td>\r\n<td>0<\/td>\r\n<td>5<\/td>\r\n<td>10<\/td>\r\n<td>15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>h<\/em>(<em>x<\/em>)<\/strong><\/td>\r\n<td>5<\/td>\r\n<td>30<\/td>\r\n<td>105<\/td>\r\n<td>230<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n17.\r\n<table id=\"Table_02_01_06\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'f(x)'. Reading the remaining rows as ordered pairs (i.e., (x, f(x)), we have the following values: (0,- 5), (5, 20), (10, 45), and (15, 70).\"><colgroup> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><strong><em>x<\/em><\/strong><\/td>\r\n<td>0<\/td>\r\n<td>5<\/td>\r\n<td>10<\/td>\r\n<td>15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>f<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\r\n<td>\u20135<\/td>\r\n<td>20<\/td>\r\n<td>45<\/td>\r\n<td>70<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n18.\r\n<table id=\"Table_02_01_07\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'k(x)'. Reading the remaining rows as ordered pairs (i.e., (x, k(x)), we have the following values: (5, 13), (10, 28), (20, 58), and (25, 73).\"><colgroup> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><strong><em>x<\/em><\/strong><\/td>\r\n<td>5<\/td>\r\n<td>10<\/td>\r\n<td>20<\/td>\r\n<td>25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>k<\/em>(<em>x<\/em>)<\/strong><\/td>\r\n<td>28<\/td>\r\n<td>13<\/td>\r\n<td>58<\/td>\r\n<td>73<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n19.\r\n<table id=\"Table_02_01_08\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'g(x)'. Reading the remaining rows as ordered pairs (i.e., (x, g(x)), we have the following values: (0, 6), (5, -10), (10, -25), and (15, -40).\"><colgroup> <col \/> <col \/> <col \/> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><em><strong>x<\/strong><\/em><\/td>\r\n<td>0<\/td>\r\n<td>2<\/td>\r\n<td>4<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>g<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\r\n<td>6<\/td>\r\n<td>\u201319<\/td>\r\n<td>\u201344<\/td>\r\n<td>\u201369<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n20.\r\n<table id=\"Table_02_01_09\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'h(x)'. Reading the remaining rows as ordered pairs (i.e., (x, h(x)), we have the following values: (2, 13), (4, 23), (8, 43), and (10, 53).\"><colgroup> <col \/> <col \/> <col \/> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><em><strong>x<\/strong><\/em><\/td>\r\n<td>2<\/td>\r\n<td>4<\/td>\r\n<td>6<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>f<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\r\n<td>\u20134<\/td>\r\n<td>16<\/td>\r\n<td>36<\/td>\r\n<td>56<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n21.\r\n<table id=\"Table_02_01_10\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'f(x)'. Reading the remaining rows as ordered pairs (i.e., (x, f(x)), we have the following values: (2, -4), (4, 16), (6, 36), and (8, 56).\"><colgroup> <col \/> <col \/> <col \/> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><strong><em>x<\/em><\/strong><\/td>\r\n<td>2<\/td>\r\n<td>4<\/td>\r\n<td>6<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>f<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\r\n<td>\u20134<\/td>\r\n<td>16<\/td>\r\n<td>36<\/td>\r\n<td>56<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n22.\r\n<table id=\"Table_02_01_11\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'k(x)'. Reading the remaining rows as ordered pairs (i.e., (x, k(x)), we have the following values: (0, 6), (2, 31), (6, 106), and (8, 231).\"><colgroup> <col \/> <col \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><em><strong>x<\/strong><\/em><\/td>\r\n<td>0<\/td>\r\n<td>2<\/td>\r\n<td>6<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong><em>k<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\r\n<td>6<\/td>\r\n<td>31<\/td>\r\n<td>106<\/td>\r\n<td>231<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n23.\u00a0Find the value of <em>x<\/em>\u00a0if a linear function goes through the following points and has the following slope: [latex]\\left(x,2\\right),\\left(-4,6\\right),m=3[\/latex]\r\n\r\n24.\u00a0Find the value of <em>y<\/em> if a linear function goes through the following points and has the following slope: [latex]\\left(10,y\\right),\\left(25,100\\right),m=-5[\/latex]\r\n\r\n25. Find the equation of the line that passes through the following points: [latex]\\left(a,\\text{ }b\\right)[\/latex] and [latex]\\left(a,\\text{ }b+1\\right)[\/latex]\r\n\r\n26.\u00a0Find the equation of the line that passes through the following points: [latex]\\left(2a,\\text{ }b\\right)[\/latex] and [latex]\\left(a,\\text{ }b+1\\right)[\/latex]\r\n\r\n27. Find the equation of the line that passes through the following points: [latex]\\left(a,\\text{ }0\\right)[\/latex] and [latex]\\left(c,\\text{ }d\\right)[\/latex]\r\n\r\nFor the following exercises, match the given linear equation with its graph.\r\n<img class=\" aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005147\/CNX_Precalc_Figure_02_02_201.jpg\" alt=\"\" \/>\r\n\r\n1. [latex]f\\left(x\\right)=-2x - 1[\/latex]\r\n\r\n2. [latex]f\\left(x\\right)=-x - 1[\/latex]\r\n\r\n3. [latex]f\\left(x\\right)=2[\/latex]\r\n\r\n4.\u00a0[latex]f\\left(x\\right)=-\\frac{1}{2}x - 1[\/latex]\r\n\r\n5. [latex]f\\left(x\\right)=3x+2[\/latex]\r\n\r\n6.\u00a0[latex]f\\left(x\\right)=2+x[\/latex]\r\n\r\nFor the following exercises, sketch a line with the given features.\r\n\r\n7. An x-intercept of [latex]\\left(-\\text{2},\\text{ 0}\\right)[\/latex] and y-intercept of [latex]\\left(0,\\text{ 4}\\right)[\/latex]\r\n\r\n8.\u00a0A y-intercept of [latex]\\left(0,\\text{ 7}\\right)[\/latex] and slope [latex]-\\frac{3}{2}[\/latex]\r\n\r\n9. A y-intercept of [latex]\\left(0,\\text{ 3}\\right)[\/latex] and slope [latex]\\frac{2}{5}[\/latex]\r\n\r\n10.\u00a0Passing through the points [latex]\\left(-\\text{6},\\text{ -2}\\right)[\/latex] and [latex]\\left(\\text{6},\\text{ -6}\\right)[\/latex]\r\n\r\n11. Passing through the points [latex]\\left(-\\text{3},\\text{ -4}\\right)[\/latex] and [latex]\\left(\\text{3},\\text{ 0}\\right)[\/latex]\r\n\r\nFor the following exercises, sketch the graph of each equation.\r\n\r\n12. [latex]f\\left(x\\right)=-2x - 1[\/latex]\r\n\r\n13. [latex]g\\left(x\\right)=-3x+2[\/latex]\r\n\r\n14. [latex]h\\left(x\\right)=\\frac{1}{3}x+2[\/latex]\r\n\r\n15. [latex]k\\left(x\\right)=\\frac{2}{3}x - 3[\/latex]\r\n\r\n16. [latex]f\\left(t\\right)=3+2t[\/latex]\r\n\r\n17. [latex]p\\left(t\\right)=-2+3t[\/latex]\r\n\r\n18.\u00a0[latex]x=3[\/latex]\r\n\r\n19. [latex]x=-2[\/latex]\r\n\r\n20. [latex]r\\left(x\\right)=4[\/latex]\r\n\r\n21. [latex]q\\left(x\\right)=3[\/latex]\r\n\r\n22. [latex]4x=-9y+36[\/latex]\r\n\r\n23. [latex]\\frac{x}{3}-\\frac{y}{4}=1[\/latex]\r\n\r\n24. [latex]3x - 5y=15[\/latex]\r\n\r\n25. [latex]3x=15[\/latex]\r\n\r\n26. [latex]3y=12[\/latex]\r\n\r\nFor the following exercises, write the equation of the line shown in the graph.\r\n\r\n27.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005149\/CNX_Precalc_Figure_02_02_222.jpg\" alt=\"\" \/>\r\n\r\n28.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005150\/CNX_Precalc_Figure_02_02_223.jpg\" alt=\"\" \/>\r\n\r\n29.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005150\/CNX_Precalc_Figure_02_02_224.jpg\" alt=\"\" \/>\r\n\r\n30.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005150\/CNX_Precalc_Figure_02_02_225.jpg\" alt=\"\" \/>","rendered":"<p>For the following exercises, find the slope of the line that passes through the two given points.<\/p>\n<p>1. [latex]\\left(2,\\text{ }4\\right)[\/latex] and [latex]\\left(4,\\text{ 10}\\right)[\/latex]<\/p>\n<p>2.\u00a0[latex]\\left(1,\\text{ 5}\\right)[\/latex] and [latex]\\left(4,\\text{ 11}\\right)[\/latex]<\/p>\n<p>3. [latex]\\left(-1,\\text{4}\\right)[\/latex] and [latex]\\left(5,\\text{2}\\right)[\/latex]<\/p>\n<p>4. [latex]\\left(8,-2\\right)[\/latex] and [latex]\\left(4,6\\right)[\/latex]<\/p>\n<p>5. [latex]\\left(6,\\text{ }11\\right)[\/latex] and [latex]\\left(-4, 3\\right)[\/latex]<\/p>\n<p>For the following exercises, find the slope of the lines graphed.<\/p>\n<p>6.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005131\/CNX_Precalc_Figure_02_01_201.jpg\" alt=\"\" \/><\/p>\n<p>7.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005132\/CNX_Precalc_Figure_02_01_202.jpg\" alt=\"\" \/><\/p>\n<p>8.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005132\/CNX_Precalc_Figure_02_01_203.jpg\" alt=\"\" \/><\/p>\n<p>For the following exercises, write an equation for the lines graphed.<\/p>\n<p>9.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005132\/CNX_Precalc_Figure_02_01_205.jpg\" alt=\"\" \/><\/p>\n<p>10.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_206.jpg\" alt=\"\" \/><\/p>\n<p>11.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_207.jpg\" alt=\"\" \/><\/p>\n<p>12.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_208.jpg\" alt=\"\" \/><\/p>\n<p>13.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005133\/CNX_Precalc_Figure_02_01_209.jpg\" alt=\"\" \/><\/p>\n<p>14.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005134\/CNX_Precalc_Figure_02_01_210.jpg\" alt=\"\" \/><\/p>\n<p>For the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear equation that models the data.<\/p>\n<p>15.<\/p>\n<table id=\"Table_02_01_04\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'g(x)'. Reading the remaining rows as ordered pairs (i.e., (x, g(x)), we have the following values: (0, 5), (5, -10), (10, -25), and (15, -40).\">\n<colgroup>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><strong><em>x<\/em><\/strong><\/td>\n<td>0<\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>15<\/td>\n<\/tr>\n<tr>\n<td><strong><em>g<\/em>(<em>x<\/em>)<\/strong><\/td>\n<td>5<\/td>\n<td>\u201310<\/td>\n<td>\u201325<\/td>\n<td>\u201340<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>16.<\/p>\n<table id=\"Table_02_01_05\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'h(x)'. Reading the remaining rows as ordered pairs (i.e., (x, h(x)), we have the following values: (0, 5), (5, 30), (10, 105), and (15, 230).\">\n<colgroup>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><strong><em>x<\/em><\/strong><\/td>\n<td>0<\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>15<\/td>\n<\/tr>\n<tr>\n<td><strong><em>h<\/em>(<em>x<\/em>)<\/strong><\/td>\n<td>5<\/td>\n<td>30<\/td>\n<td>105<\/td>\n<td>230<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>17.<\/p>\n<table id=\"Table_02_01_06\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'f(x)'. Reading the remaining rows as ordered pairs (i.e., (x, f(x)), we have the following values: (0,- 5), (5, 20), (10, 45), and (15, 70).\">\n<colgroup>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><strong><em>x<\/em><\/strong><\/td>\n<td>0<\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>15<\/td>\n<\/tr>\n<tr>\n<td><strong><em>f<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\n<td>\u20135<\/td>\n<td>20<\/td>\n<td>45<\/td>\n<td>70<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>18.<\/p>\n<table id=\"Table_02_01_07\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'k(x)'. Reading the remaining rows as ordered pairs (i.e., (x, k(x)), we have the following values: (5, 13), (10, 28), (20, 58), and (25, 73).\">\n<colgroup>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><strong><em>x<\/em><\/strong><\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>20<\/td>\n<td>25<\/td>\n<\/tr>\n<tr>\n<td><strong><em>k<\/em>(<em>x<\/em>)<\/strong><\/td>\n<td>28<\/td>\n<td>13<\/td>\n<td>58<\/td>\n<td>73<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>19.<\/p>\n<table id=\"Table_02_01_08\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'g(x)'. Reading the remaining rows as ordered pairs (i.e., (x, g(x)), we have the following values: (0, 6), (5, -10), (10, -25), and (15, -40).\">\n<colgroup>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><em><strong>x<\/strong><\/em><\/td>\n<td>0<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td><strong><em>g<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\n<td>6<\/td>\n<td>\u201319<\/td>\n<td>\u201344<\/td>\n<td>\u201369<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>20.<\/p>\n<table id=\"Table_02_01_09\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'h(x)'. Reading the remaining rows as ordered pairs (i.e., (x, h(x)), we have the following values: (2, 13), (4, 23), (8, 43), and (10, 53).\">\n<colgroup>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><em><strong>x<\/strong><\/em><\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>6<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td><strong><em>f<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\n<td>\u20134<\/td>\n<td>16<\/td>\n<td>36<\/td>\n<td>56<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>21.<\/p>\n<table id=\"Table_02_01_10\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'f(x)'. Reading the remaining rows as ordered pairs (i.e., (x, f(x)), we have the following values: (2, -4), (4, 16), (6, 36), and (8, 56).\">\n<colgroup>\n<col \/>\n<col \/>\n<col \/>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><strong><em>x<\/em><\/strong><\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>6<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td><strong><em>f<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\n<td>\u20134<\/td>\n<td>16<\/td>\n<td>36<\/td>\n<td>56<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>22.<\/p>\n<table id=\"Table_02_01_11\" class=\"unnumbered\" summary=\"Two columns and five rows. The first column is labeled, 'x'. The second column is labeled, 'k(x)'. Reading the remaining rows as ordered pairs (i.e., (x, k(x)), we have the following values: (0, 6), (2, 31), (6, 106), and (8, 231).\">\n<colgroup>\n<col \/>\n<col \/><\/colgroup>\n<tbody>\n<tr>\n<td><em><strong>x<\/strong><\/em><\/td>\n<td>0<\/td>\n<td>2<\/td>\n<td>6<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td><strong><em>k<\/em>(<em>x<\/em>)\u00a0<\/strong><\/td>\n<td>6<\/td>\n<td>31<\/td>\n<td>106<\/td>\n<td>231<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>23.\u00a0Find the value of <em>x<\/em>\u00a0if a linear function goes through the following points and has the following slope: [latex]\\left(x,2\\right),\\left(-4,6\\right),m=3[\/latex]<\/p>\n<p>24.\u00a0Find the value of <em>y<\/em> if a linear function goes through the following points and has the following slope: [latex]\\left(10,y\\right),\\left(25,100\\right),m=-5[\/latex]<\/p>\n<p>25. Find the equation of the line that passes through the following points: [latex]\\left(a,\\text{ }b\\right)[\/latex] and [latex]\\left(a,\\text{ }b+1\\right)[\/latex]<\/p>\n<p>26.\u00a0Find the equation of the line that passes through the following points: [latex]\\left(2a,\\text{ }b\\right)[\/latex] and [latex]\\left(a,\\text{ }b+1\\right)[\/latex]<\/p>\n<p>27. Find the equation of the line that passes through the following points: [latex]\\left(a,\\text{ }0\\right)[\/latex] and [latex]\\left(c,\\text{ }d\\right)[\/latex]<\/p>\n<p>For the following exercises, match the given linear equation with its graph.<br \/>\n<img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005147\/CNX_Precalc_Figure_02_02_201.jpg\" alt=\"\" \/><\/p>\n<p>1. [latex]f\\left(x\\right)=-2x - 1[\/latex]<\/p>\n<p>2. [latex]f\\left(x\\right)=-x - 1[\/latex]<\/p>\n<p>3. [latex]f\\left(x\\right)=2[\/latex]<\/p>\n<p>4.\u00a0[latex]f\\left(x\\right)=-\\frac{1}{2}x - 1[\/latex]<\/p>\n<p>5. [latex]f\\left(x\\right)=3x+2[\/latex]<\/p>\n<p>6.\u00a0[latex]f\\left(x\\right)=2+x[\/latex]<\/p>\n<p>For the following exercises, sketch a line with the given features.<\/p>\n<p>7. An x-intercept of [latex]\\left(-\\text{2},\\text{ 0}\\right)[\/latex] and y-intercept of [latex]\\left(0,\\text{ 4}\\right)[\/latex]<\/p>\n<p>8.\u00a0A y-intercept of [latex]\\left(0,\\text{ 7}\\right)[\/latex] and slope [latex]-\\frac{3}{2}[\/latex]<\/p>\n<p>9. A y-intercept of [latex]\\left(0,\\text{ 3}\\right)[\/latex] and slope [latex]\\frac{2}{5}[\/latex]<\/p>\n<p>10.\u00a0Passing through the points [latex]\\left(-\\text{6},\\text{ -2}\\right)[\/latex] and [latex]\\left(\\text{6},\\text{ -6}\\right)[\/latex]<\/p>\n<p>11. Passing through the points [latex]\\left(-\\text{3},\\text{ -4}\\right)[\/latex] and [latex]\\left(\\text{3},\\text{ 0}\\right)[\/latex]<\/p>\n<p>For the following exercises, sketch the graph of each equation.<\/p>\n<p>12. [latex]f\\left(x\\right)=-2x - 1[\/latex]<\/p>\n<p>13. [latex]g\\left(x\\right)=-3x+2[\/latex]<\/p>\n<p>14. [latex]h\\left(x\\right)=\\frac{1}{3}x+2[\/latex]<\/p>\n<p>15. [latex]k\\left(x\\right)=\\frac{2}{3}x - 3[\/latex]<\/p>\n<p>16. [latex]f\\left(t\\right)=3+2t[\/latex]<\/p>\n<p>17. [latex]p\\left(t\\right)=-2+3t[\/latex]<\/p>\n<p>18.\u00a0[latex]x=3[\/latex]<\/p>\n<p>19. [latex]x=-2[\/latex]<\/p>\n<p>20. [latex]r\\left(x\\right)=4[\/latex]<\/p>\n<p>21. [latex]q\\left(x\\right)=3[\/latex]<\/p>\n<p>22. [latex]4x=-9y+36[\/latex]<\/p>\n<p>23. [latex]\\frac{x}{3}-\\frac{y}{4}=1[\/latex]<\/p>\n<p>24. [latex]3x - 5y=15[\/latex]<\/p>\n<p>25. [latex]3x=15[\/latex]<\/p>\n<p>26. [latex]3y=12[\/latex]<\/p>\n<p>For the following exercises, write the equation of the line shown in the graph.<\/p>\n<p>27.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005149\/CNX_Precalc_Figure_02_02_222.jpg\" alt=\"\" \/><\/p>\n<p>28.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005150\/CNX_Precalc_Figure_02_02_223.jpg\" alt=\"\" \/><\/p>\n<p>29.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005150\/CNX_Precalc_Figure_02_02_224.jpg\" alt=\"\" \/><\/p>\n<p>30.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03005150\/CNX_Precalc_Figure_02_02_225.jpg\" alt=\"\" \/><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-15273\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at: http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at: http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15273","chapter","type-chapter","status-publish","hentry"],"part":15410,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15273","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15273\/revisions"}],"predecessor-version":[{"id":15960,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15273\/revisions\/15960"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/15410"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15273\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15273"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15273"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15273"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}