Worksheet for graphing linear equations in slope-intercept form.

Let's solve this step-by-step. The task is to graph each line given in slope-intercept form, which is:

$$
y = mx + b
$$

Where:
- $ m $ is the slope (rise over run),
- $ b $ is the y-intercept (where the line crosses the y-axis).

We'll go through each equation, identify the slope and y-intercept, plot the y-intercept, then use the slope to find a second point, and draw the line.

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🔷 General Steps for Graphing:

1. Plot the y-intercept $(0, b)$.
2. Use the slope $m$ to find another point:
- If $m = \frac{a}{b}$, go up $a$ units and right $b$ units (or down if negative).
3. Draw a straight line through the two points.

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Let’s solve each one:

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1.) $ y = 5x + 2 $

- Slope: $5 = \frac{5}{1}$
- Y-intercept: $ (0, 2) $
- From $ (0, 2) $, go up 5, right 1 → $ (1, 7) $
- Plot both points and draw the line.

✔ Graph: Starts at (0,2), goes steeply upward.

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2.) $ y = -\frac{2}{3}x - 5 $

- Slope: $-\frac{2}{3}$
- Y-intercept: $ (0, -5) $
- From $ (0, -5) $, go down 2, right 3 → $ (3, -7) $
- Or: up 2, left 3 → $ (-3, -3) $

✔ Graph: Starts at (0,-5), slopes downward gently.

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3.) $ y = -\frac{4}{7}x + 1 $

- Slope: $-\frac{4}{7}$
- Y-intercept: $ (0, 1) $
- From $ (0, 1) $, go down 4, right 7 → $ (7, -3) $
- Or: up 4, left 7 → $ (-7, 5) $

✔ Graph: Starts at (0,1), slopes downward gradually.

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4.) $ y = x + 8 $

- Slope: $1 = \frac{1}{1}$
- Y-intercept: $ (0, 8) $
- From $ (0, 8) $, go up 1, right 1 → $ (1, 9) $

✔ Graph: Starts at (0,8), goes diagonally upward with a 45° angle.

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5.) $ y = \frac{8}{5}x - 2 $

- Slope: $\frac{8}{5}$
- Y-intercept: $ (0, -2) $
- From $ (0, -2) $, go up 8, right 5 → $ (5, 6) $

✔ Graph: Starts at (0,-2), rises steeply.

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6.) $ y = -x + 4 $

- Slope: $-1 = \frac{-1}{1}$
- Y-intercept: $ (0, 4) $
- From $ (0, 4) $, go down 1, right 1 → $ (1, 3) $

✔ Graph: Starts at (0,4), goes downward at 45°.

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7.) $ y = \frac{1}{7}x + 9 $

- Slope: $\frac{1}{7}$
- Y-intercept: $ (0, 9) $
- From $ (0, 9) $, go up 1, right 7 → $ (7, 10) $

✔ Graph: Starts at (0,9), very shallow upward slope.

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8.) $ y = -\frac{5}{4}x - 3 $

- Slope: $-\frac{5}{4}$
- Y-intercept: $ (0, -3) $
- From $ (0, -3) $, go down 5, right 4 → $ (4, -8) $
- Or: up 5, left 4 → $ (-4, 2) $

✔ Graph: Starts at (0,-3), slopes downward fairly steeply.

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✔ Summary of Key Points for Each Line:

| Equation | Slope | Y-Intercept | Direction |
|--------|-------|-------------|-----------|
| 1. $ y = 5x + 2 $ | ↑5/1 | (0,2) | Steep up |
| 2. $ y = -\frac{2}{3}x - 5 $ | ↓2/3 | (0,-5) | Down gentle |
| 3. $ y = -\frac{4}{7}x + 1 $ | ↓4/7 | (0,1) | Down gentle |
| 4. $ y = x + 8 $ | ↑1/1 | (0,8) | Diagonal up |
| 5. $ y = \frac{8}{5}x - 2 $ | ↑8/5 | (0,-2) | Steep up |
| 6. $ y = -x + 4 $ | ↓1/1 | (0,4) | Diagonal down |
| 7. $ y = \frac{1}{7}x + 9 $ | ↑1/7 | (0,9) | Very shallow up |
| 8. $ y = -\frac{5}{4}x - 3 $ | ↓5/4 | (0,-3) | Steep down |

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📝 How to Graph on Paper:

For each problem:
1. Mark the y-intercept on the grid.
2. Use rise/run to move to next point.
3. Draw a straight line through them.

> 💡 Tip: Always check your work by plugging in a value like $x=1$ into the equation to verify the point lies on the line.

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Since I can't draw directly here, you can now use this guide to sketch each graph accurately on the provided coordinate planes.

Would you like me to generate a visual description or ASCII approximation of any specific graph?