Worksheet for determining y-intercept, x-intercept, and slope from linear equation graphs.

Let's solve each of the four linear graphs shown in the worksheet. We'll determine:

- Y-intercept: Where the line crosses the y-axis (x = 0)
- X-intercept: Where the line crosses the x-axis (y = 0)
- Slope: Rise over run, calculated as $ m = \frac{\text{change in } y}{\text{change in } x} $

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Graph 1 (Top Left - Blue Line)

Step 1: Y-intercept
- The line crosses the y-axis at $ y = -2 $
- So, y-intercept = -2

Step 2: X-intercept
- The line crosses the x-axis at $ x = -4 $
- So, x-intercept = -4

Step 3: Slope
- Pick two points on the line: $ (-4, 0) $ and $ (0, -2) $
- Change in y: $ -2 - 0 = -2 $
- Change in x: $ 0 - (-4) = 4 $
- Slope $ m = \frac{-2}{4} = -\frac{1}{2} $

✔ Answer:
- y-intercept: $-2$
- x-intercept: $-4$
- Slope: $-\frac{1}{2}$

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Graph 2 (Top Right - Red Line)

Step 1: Y-intercept
- The line crosses the y-axis at $ y = 5 $
- So, y-intercept = 5

Step 2: X-intercept
- The line crosses the x-axis at $ x = 2 $
- So, x-intercept = 2

Step 3: Slope
- Pick two points: $ (2, 0) $ and $ (0, 5) $
- Change in y: $ 5 - 0 = 5 $
- Change in x: $ 0 - 2 = -2 $
- Slope $ m = \frac{5}{-2} = -\frac{5}{2} $

✔ Answer:
- y-intercept: $5$
- x-intercept: $2$
- Slope: $-\frac{5}{2}$

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Graph 3 (Bottom Left - Green Line)

Step 1: Y-intercept
- The line crosses the y-axis at $ y = -4 $
- So, y-intercept = -4

Step 2: X-intercept
- The line crosses the x-axis at $ x = -2 $
- So, x-intercept = -2

Step 3: Slope
- Points: $ (-2, 0) $ and $ (0, -4) $
- Change in y: $ -4 - 0 = -4 $
- Change in x: $ 0 - (-2) = 2 $
- Slope $ m = \frac{-4}{2} = -2 $

✔ Answer:
- y-intercept: $-4$
- x-intercept: $-2$
- Slope: $-2$

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Graph 4 (Bottom Right - Purple Line)

Step 1: Y-intercept
- The line crosses the y-axis at $ y = -3 $
- So, y-intercept = -3

Step 2: X-intercept
- The line crosses the x-axis at $ x = 4 $
- So, x-intercept = 4

Step 3: Slope
- Points: $ (4, 0) $ and $ (0, -3) $
- Change in y: $ -3 - 0 = -3 $
- Change in x: $ 0 - 4 = -4 $
- Slope $ m = \frac{-3}{-4} = \frac{3}{4} $

✔ Answer:
- y-intercept: $-3$
- x-intercept: $4$
- Slope: $\frac{3}{4}$

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✔ Final Answers Summary:

| Graph | y-intercept | x-intercept | Slope |
|-------|-------------|-------------|--------|
| 1 (Blue) | -2 | -4 | $-\frac{1}{2}$ |
| 2 (Red) | 5 | 2 | $-\frac{5}{2}$ |
| 3 (Green) | -4 | -2 | $-2$ |
| 4 (Purple) | -3 | 4 | $\frac{3}{4}$ |

You can now fill these values into the worksheet accordingly.

Let me know if you'd like a visual explanation or help writing the equations!