Worksheet for finding slope and y-intercept from linear graphs.

Let's solve each problem step by step. We are asked to find the slope and y-intercept of each line shown in the graphs.

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🔹 How to find slope and y-intercept from a graph:

1. Y-intercept (b):
- This is the point where the line crosses the y-axis (i.e., when $ x = 0 $).
- Read the y-coordinate at that point.

2. Slope (m):
- Slope = $ \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x} $
- Pick two points on the line.
- Count how many units you go up/down (rise) and left/right (run) between them.
- Simplify the ratio.

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Let’s analyze each graph:

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Graph 1

- The line passes through:
- $(-4, 0)$ and $(0, 3)$
- Y-intercept: When $x = 0$, $y = 3$ → $ \boxed{3} $
- Slope: From $(-4, 0)$ to $(0, 3)$:
- Rise = $3 - 0 = 3$
- Run = $0 - (-4) = 4$
- Slope = $ \frac{3}{4} $

✔ Slope: $ \frac{3}{4} $, Y-intercept: $ 3 $

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Graph 2

- Points on line: $(0, 2)$ and $(5, 0)$
- Y-intercept: $x = 0$, $y = 2$ → $ \boxed{2} $
- Slope: From $(0, 2)$ to $(5, 0)$:
- Rise = $0 - 2 = -2$
- Run = $5 - 0 = 5$
- Slope = $ \frac{-2}{5} = -\frac{2}{5} $

✔ Slope: $ -\frac{2}{5} $, Y-intercept: $ 2 $

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Graph 3

- Points: $(2, 0)$ and $(0, -4)$
- Y-intercept: $x = 0$, $y = -4$ → $ \boxed{-4} $
- Slope: From $(2, 0)$ to $(0, -4)$:
- Rise = $-4 - 0 = -4$
- Run = $0 - 2 = -2$
- Slope = $ \frac{-4}{-2} = 2 $

✔ Slope: $ 2 $, Y-intercept: $ -4 $

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Graph 4

- Points: $(0, 1)$ and $(3, -5)$
- Y-intercept: $x = 0$, $y = 1$ → $ \boxed{1} $
- Slope: From $(0, 1)$ to $(3, -5)$:
- Rise = $-5 - 1 = -6$
- Run = $3 - 0 = 3$
- Slope = $ \frac{-6}{3} = -2 $

✔ Slope: $ -2 $, Y-intercept: $ 1 $

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Graph 5

- Points: $(0, -1)$ and $(3, 4)$
- Y-intercept: $x = 0$, $y = -1$ → $ \boxed{-1} $
- Slope: From $(0, -1)$ to $(3, 4)$:
- Rise = $4 - (-1) = 5$
- Run = $3 - 0 = 3$
- Slope = $ \frac{5}{3} $

✔ Slope: $ \frac{5}{3} $, Y-intercept: $ -1 $

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Graph 6

- Points: $(0, 1)$ and $(2, 4)$
- Y-intercept: $x = 0$, $y = 1$ → $ \boxed{1} $
- Slope: From $(0, 1)$ to $(2, 4)$:
- Rise = $4 - 1 = 3$
- Run = $2 - 0 = 2$
- Slope = $ \frac{3}{2} $

✔ Slope: $ \frac{3}{2} $, Y-intercept: $ 1 $

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✔ Final Answers:

| Graph | Slope | Y-intercept |
|-------|--------------|-------------|
| 1 | $ \frac{3}{4} $ | 3 |
| 2 | $ -\frac{2}{5} $ | 2 |
| 3 | $ 2 $ | -4 |
| 4 | $ -2 $ | 1 |
| 5 | $ \frac{5}{3} $ | -1 |
| 6 | $ \frac{3}{2} $ | 1 |

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Let me know if you'd like these written in equation form ($y = mx + b$)!