Graphing Linear Equations in Slope-Intercept Form | Worksheet ... - Free Printable

Let's solve the problem step by step. You're asked to graph linear equations in slope-intercept form, which is:

$$
y = mx + b
$$

Where:
- $ m $ is the slope
- $ b $ is the y-intercept

We’ll go through each equation one by one and graph it on the coordinate plane.

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🔹 Equation 1: $ y = 2x + 3 $

Step 1: Identify slope and y-intercept
- Slope ($ m $) = 2 → rise over run = $ \frac{2}{1} $
- Y-intercept ($ b $) = 3 → point: $ (0, 3) $

Step 2: Plot the y-intercept
- Start at $ (0, 3) $ on the y-axis.

Step 3: Use the slope to find another point
- From $ (0, 3) $, go up 2 units, right 1 unit → $ (1, 5) $
- Plot this point.

Step 4: Draw a straight line through both points

✔ Graph: Line passing through $ (0, 3) $ and $ (1, 5) $, going upward.

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🔹 Equation 2: $ y = \frac{1}{2}x - 6 $

Step 1: Identify slope and y-intercept
- Slope ($ m $) = $ \frac{1}{2} $ → rise over run = $ \frac{1}{2} $
- Y-intercept ($ b $) = -6 → point: $ (0, -6) $

Step 2: Plot the y-intercept
- Start at $ (0, -6) $

Step 3: Use the slope to find another point
- From $ (0, -6) $, go up 1 unit, right 2 units → $ (2, -5) $
- Plot this point.

Step 4: Draw a straight line through both points

✔ Graph: Line passing through $ (0, -6) $ and $ (2, -5) $, rising slowly.

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🔹 Equation 3: $ y = -4x - 2 $

Step 1: Identify slope and y-intercept
- Slope ($ m $) = -4 → rise over run = $ \frac{-4}{1} $
- Y-intercept ($ b $) = -2 → point: $ (0, -2) $

Step 2: Plot the y-intercept
- Start at $ (0, -2) $

Step 3: Use the slope to find another point
- From $ (0, -2) $, go down 4 units, right 1 unit → $ (1, -6) $
- Plot this point.

Step 4: Draw a straight line through both points

✔ Graph: Line passing through $ (0, -2) $ and $ (1, -6) $, steeply decreasing.

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🔹 Equation 4: $ y = \frac{3}{4}x $

Step 1: Identify slope and y-intercept
- Slope ($ m $) = $ \frac{3}{4} $
- Y-intercept ($ b $) = 0 → point: $ (0, 0) $

Step 2: Plot the y-intercept
- Start at origin $ (0, 0) $

Step 3: Use the slope to find another point
- From $ (0, 0) $, go up 3 units, right 4 units → $ (4, 3) $
- Plot this point.

Step 4: Draw a straight line through both points

✔ Graph: Line passing through $ (0, 0) $ and $ (4, 3) $, rising gently.

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✔ Summary of How to Graph Each:

| Equation | Slope | Y-intercept | Starting Point | Next Point |
|--------|-------|-------------|----------------|------------|
| $ y = 2x + 3 $ | 2 | 3 | $ (0, 3) $ | $ (1, 5) $ |
| $ y = \frac{1}{2}x - 6 $ | $ \frac{1}{2} $ | -6 | $ (0, -6) $ | $ (2, -5) $ |
| $ y = -4x - 2 $ | -4 | -2 | $ (0, -2) $ | $ (1, -6) $ |
| $ y = \frac{3}{4}x $ | $ \frac{3}{4} $ | 0 | $ (0, 0) $ | $ (4, 3) $ |

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📌 Tips for Graphing:

- Always start with the y-intercept.
- Use the slope to move from that point.
- Draw a straight line through the two points.
- Extend the line in both directions with arrows.

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Since I can't draw directly on your image, you should now:
1. On each grid, plot the y-intercept.
2. Use the slope to find a second point.
3. Draw a line through both points.

Let me know if you'd like a visual description or help checking your work!