Slope intercept form | Worksheetzone - Free Printable

Let's solve each part of the worksheet step by step. We are asked to find the slope-intercept form of the line for each graph, which is:

$$
y = mx + b
$$

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

We will determine the slope and y-intercept from each graph.

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a.

- The line passes through points: (-2, 2), (0, 1), and (2, 0)
- Y-intercept: The line crosses the y-axis at $ y = 1 $ → $ b = 1 $
- Slope: Use two points, say (0,1) and (2,0):
$$
m = \frac{0 - 1}{2 - 0} = \frac{-1}{2} = -\frac{1}{2}
$$
- Equation: $ y = -\frac{1}{2}x + 1 $

✔ Answer:
- Slope = $-\frac{1}{2}$
- y-intercept = 1
- Equation: $ y = -\frac{1}{2}x + 1 $

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b.

- Line passes through: (-2, -3), (0, 0), (2, 3)
- Y-intercept: Crosses y-axis at (0,0) → $ b = 0 $
- Slope: Use (0,0) and (2,3):
$$
m = \frac{3 - 0}{2 - 0} = \frac{3}{2}
$$
- Equation: $ y = \frac{3}{2}x $

✔ Answer:
- Slope = $ \frac{3}{2} $
- y-intercept = 0
- Equation: $ y = \frac{3}{2}x $

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c.

- Points on the line: (-4, 2), (0, 1), (4, 0)
- Y-intercept: At $ x = 0 $, $ y = 1 $ → $ b = 1 $
- Slope: Use (0,1) and (4,0):
$$
m = \frac{0 - 1}{4 - 0} = \frac{-1}{4} = -\frac{1}{4}
$$
- Equation: $ y = -\frac{1}{4}x + 1 $

✔ Answer:
- Slope = $-\frac{1}{4}$
- y-intercept = 1
- Equation: $ y = -\frac{1}{4}x + 1 $

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d.

- Points: (-2, -3), (0, -1), (2, 1), (4, 3)
- Y-intercept: At $ x = 0 $, $ y = -1 $ → $ b = -1 $
- Slope: Use (0,-1) and (2,1):
$$
m = \frac{1 - (-1)}{2 - 0} = \frac{2}{2} = 1
$$
- Equation: $ y = x - 1 $

✔ Answer:
- Slope = 1
- y-intercept = -1
- Equation: $ y = x - 1 $

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e.

- Points: (-1, 3), (0, 2), (1, 1), (2, 0)
- Y-intercept: At $ x = 0 $, $ y = 2 $ → $ b = 2 $
- Slope: Use (0,2) and (1,1):
$$
m = \frac{1 - 2}{1 - 0} = \frac{-1}{1} = -1
$$
- Equation: $ y = -x + 2 $

✔ Answer:
- Slope = -1
- y-intercept = 2
- Equation: $ y = -x + 2 $

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f.

- Points: (-2, -1), (0, 1), (2, 3), (4, 5)
- Y-intercept: At $ x = 0 $, $ y = 1 $ → $ b = 1 $
- Slope: Use (0,1) and (2,3):
$$
m = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1
$$
- Equation: $ y = x + 1 $

✔ Answer:
- Slope = 1
- y-intercept = 1
- Equation: $ y = x + 1 $

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✔ Final Answers Summary:

| Graph | Slope | y-intercept | Equation |
|-------|-------------|-------------|------------------------|
| a | $-\frac{1}{2}$ | 1 | $ y = -\frac{1}{2}x + 1 $ |
| b | $ \frac{3}{2} $ | 0 | $ y = \frac{3}{2}x $ |
| c | $-\frac{1}{4}$ | 1 | $ y = -\frac{1}{4}x + 1 $ |
| d | 1 | -1 | $ y = x - 1 $ |
| e | -1 | 2 | $ y = -x + 2 $ |
| f | 1 | 1 | $ y = x + 1 $ |

Let me know if you'd like this formatted as a printable answer sheet!