G1.08: Exercises

Part I

  1. For this formula: [latex]R=-6.3+8.2\cdot{d}[/latex], tell
    1. Which variable is the output variable?
    2. Which variable is the input variable?
    3. Is it linear relationship?
    4. If it is a linear relationship, what is the slope?
    5. If it is a linear relationship, what is the y-intercept?
  2. For this formula:   [latex]R=-6.3+8.2\cdot{d}[/latex], find a three points that fit this and use them to sketch a graph.
  3. A manager is considering the cost C of printing a book based on the number of pages p. He is told that the formula for predicting the cost is linear based on the number of pages and that the y-intercept is $4.50 and the slope is $0.027. Find the formula to predict the cost from the number of pages.
  4. Find the formula for the line with slope 1.35 which has the point (5,40) on it.
  5. Find the formula for the line through (2,6) and (4,11).
    Identify the slope and y-intercept.
  6. We have been told that the amount of oatmeal needed for oatmeal cookies is linearly related to the amount of flour needed. Also, we know that if we use 3 cups of flour, we need 2 cups of oatmeal. And, of course, if we use 0 cups of flour, we will use 0 cups of oatmeal.
    1. Find the formula to predict the oatmeal needed (called M) from the flour needed (F.)
    2. Interpret the slope.
    3. Interpret the y-intercept.
  7. Find the slope and intercept of the line [latex]y=-2.32x+7.89[/latex]
  8. Find the slope and intercept of the line [latex]y=84.4+9.2x[/latex]
  9. Find the slope and intercept of the line [latex]y=1127-93x[/latex]
  10. Find the slope and the intercept of the line [latex]y=2178x-114[/latex]
  11. Find the formula for the line with slope -6.2 through the point (87.2, 112.7)
  12. Find the formula for the line through (8,5) and (13,17)
  13. Find the formula for the line through (83.8, 79.9) and (232.7, 63.4)
  14. Use a spreadsheet to approximate the equation of the line through (1,4) and (9,14).

Part II

Write your formulas for lines in point-slope form. You may make the requested graphs by hand on graph paper or using a spreadsheet.

  1. For this formula: [latex]M=12.2-4.3\cdot{z}[/latex], tell
    1. Which variable is the output variable?
    2. Which variable is the input variable?
    3. Is it linear relationship?
    4. If it is a linear relationship, what is the slope?
    5. If it is a linear relationship, what is the y-intercept?
  2. A manager has proposed that the rent on apartments in one location will be linear based on the number of square feet in the apartment. The y-intercept will be $160 and the slope will be $1.50. Find the formula to predict the rent from the number of square feet in the apartment.
  3. Janet’s recipe for split-pea soup has a linear relationship between the amount of carrots and the amount of onions.   When she uses 1.5 cups of carrots, she uses 1 cup of onions. When she uses 3 cups of carrots, she uses 2 cups of onions.
    1. Find the formula to predict the onions needed (called N) from the carrots needed (C.)
    2. Interpret the slope.
    3. Interpret the y-intercept.
  4. Find the formula for the line through the point (2,8) with slope 2.   Check this by looking at the formula to see that the slope coefficient is 2 and then also plugging in the point (2,8) to confirm that it really does fit the equation.
  5. Find the formula for the line through the point (13.3, 117.8) with slope 2.7. Check this by looking at the formula to see that the slope coefficient is 2.7 and then also plugging in the point (13.3, 117.8) to confirm that it really does fit the equation.
  6. Find the formula for line through the points (4,12) and (18,37). Check this by plugging in the point that you DID NOT use in the last step to find the intercept, and be sure that it fits the equation.
  7. Find a formula for the line through the points (82.7, 227.2) and (105.3, 304.2). Check this by plugging in the point that you DID NOT use in the last step to find the intercept, and be sure that it fits the equation.
  8. Find a formula for the line through the points (4,28) and (9,13). Check this by plugging in the point that you DID NOT use in the last step to find the intercept, and be sure that it fits the equation.
  9. Find a formula for the line through the points (58.2,102.7) and (75.8, 47.5). Check this by plugging in the point that you DID NOT use in the last step to find the intercept, and be sure that it fits the equation.
  10. Use a spreadsheet to approximate the formula for the line through the points (4,12) and (18,37). Use this to check your work in the previous problem (number 20) where you found the formula algebraically.
  11. Use a spreadsheet to approximate the formula for the line through the points (82.7, 227.2) and (105.3, 304.2). Use this to check your work in the previous problem (problem 21) where you found the formula algebraically.
  12. Use a spreadsheet to approximate the formula for the line through the points (4,28) and (9,13). Use this to check your work in the previous problem (problem 22) where you found the formula algebraically.
  13. Use a spreadsheet to approximate the formula for the line through the points (58.2,102.7) and (75.8,47.5). Use this to check your work in the previous problem (problem 23) where you found the formula algebraically.
  14. Find the formula for the line between (12,4) and (37,18). Do this by either of the two methods in Section 3. Compare the slopes of this line and the line you found in the problem 20, where you had the input and output variable switched. Are they reciprocals? (Hint: multiply them together and see if you get 1. If so, they are reciprocals.)
  15. Find a formula for the line through the points (28,4) and (13,9). Do this by either of the two methods in Section 3. Compare the slopes of this line and the line you found in problem 22, where you had the input and output variable switched. Are they reciprocals? (Hint: multiply them together and see if you get 1. If so, they are reciprocals.)