For the following exercises, find the slope of the line that passes through the two given points.
1. [latex]\left(2,\text{ }4\right)[/latex] and [latex]\left(4,\text{ 10}\right)[/latex]
2. [latex]\left(1,\text{ 5}\right)[/latex] and [latex]\left(4,\text{ 11}\right)[/latex]
3. [latex]\left(-1,\text{4}\right)[/latex] and [latex]\left(5,\text{2}\right)[/latex]
4. [latex]\left(8,-2\right)[/latex] and [latex]\left(4,6\right)[/latex]
5. [latex]\left(6,\text{ }11\right)[/latex] and [latex]\left(-4, 3\right)[/latex]
For the following exercises, find the slope of the lines graphed.
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For the following exercises, write an equation for the lines graphed.
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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.
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| x | 0 | 5 | 10 | 15 |
| g(x) | 5 | –10 | –25 | –40 |
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| x | 0 | 5 | 10 | 15 |
| h(x) | 5 | 30 | 105 | 230 |
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| x | 0 | 5 | 10 | 15 |
| f(x) | –5 | 20 | 45 | 70 |
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| x | 5 | 10 | 20 | 25 |
| k(x) | 28 | 13 | 58 | 73 |
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| x | 0 | 2 | 4 | 6 |
| g(x) | 6 | –19 | –44 | –69 |
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| x | 2 | 4 | 6 | 8 |
| f(x) | –4 | 16 | 36 | 56 |
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| x | 2 | 4 | 6 | 8 |
| f(x) | –4 | 16 | 36 | 56 |
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| x | 0 | 2 | 6 | 8 |
| k(x) | 6 | 31 | 106 | 231 |
23. Find the value of x if 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]
24. Find the value of y 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]
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]
26. Find 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]
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]
For the following exercises, match the given linear equation with its graph.
1. [latex]f\left(x\right)=-2x - 1[/latex]
2. [latex]f\left(x\right)=-x - 1[/latex]
3. [latex]f\left(x\right)=2[/latex]
4. [latex]f\left(x\right)=-\frac{1}{2}x - 1[/latex]
5. [latex]f\left(x\right)=3x+2[/latex]
6. [latex]f\left(x\right)=2+x[/latex]
For the following exercises, sketch a line with the given features.
7. An x-intercept of [latex]\left(-\text{2},\text{ 0}\right)[/latex] and y-intercept of [latex]\left(0,\text{ 4}\right)[/latex]
8. A y-intercept of [latex]\left(0,\text{ 7}\right)[/latex] and slope [latex]-\frac{3}{2}[/latex]
9. A y-intercept of [latex]\left(0,\text{ 3}\right)[/latex] and slope [latex]\frac{2}{5}[/latex]
10. Passing through the points [latex]\left(-\text{6},\text{ -2}\right)[/latex] and [latex]\left(\text{6},\text{ -6}\right)[/latex]
11. Passing through the points [latex]\left(-\text{3},\text{ -4}\right)[/latex] and [latex]\left(\text{3},\text{ 0}\right)[/latex]
For the following exercises, sketch the graph of each equation.
12. [latex]f\left(x\right)=-2x - 1[/latex]
13. [latex]g\left(x\right)=-3x+2[/latex]
14. [latex]h\left(x\right)=\frac{1}{3}x+2[/latex]
15. [latex]k\left(x\right)=\frac{2}{3}x - 3[/latex]
16. [latex]f\left(t\right)=3+2t[/latex]
17. [latex]p\left(t\right)=-2+3t[/latex]
18. [latex]x=3[/latex]
19. [latex]x=-2[/latex]
20. [latex]r\left(x\right)=4[/latex]
21. [latex]q\left(x\right)=3[/latex]
22. [latex]4x=-9y+36[/latex]
23. [latex]\frac{x}{3}-\frac{y}{4}=1[/latex]
24. [latex]3x - 5y=15[/latex]
25. [latex]3x=15[/latex]
26. [latex]3y=12[/latex]
For the following exercises, write the equation of the line shown in the graph.
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