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

17.

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

22.

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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