Worksheet for finding the slope-intercept form of a line equation using given point pairs.

Let’s solve each problem step by step. We’re finding the slope-intercept form of a line:
> y = mx + b
where:
- m is the slope (how steep the line is)
- b is the y-intercept (where the line crosses the y-axis)

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Step 1: Find the slope (m) between two points

Use this formula:
> m = (y₂ - y₁) / (x₂ - x₁)

Then plug in one point and the slope into y = mx + b to find b.

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## Problem 1: (4, -1) and (0, 5)

Slope m = (5 - (-1)) / (0 - 4) = (6) / (-4) = -3/2

Now use point (0, 5). Since x=0, that means b = 5!

✔ Equation: y = -3/2 x + 5

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## Problem 2: (6, -3) and (-2, 3)

m = (3 - (-3)) / (-2 - 6) = (6) / (-8) = -3/4

Use point (6, -3):
-3 = (-3/4)(6) + b
-3 = -18/4 + b → -3 = -9/2 + b
Add 9/2 to both sides:
b = -3 + 9/2 = (-6/2 + 9/2) = 3/2

✔ Equation: y = -3/4 x + 3/2

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## Problem 3: (3, 8) and (-2, 1)

m = (1 - 8) / (-2 - 3) = (-7) / (-5) = 7/5

Use point (3, 8):
8 = (7/5)(3) + b → 8 = 21/5 + b
b = 8 - 21/5 = 40/5 - 21/5 = 19/5

✔ Equation: y = 7/5 x + 19/5

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## Problem 4: (-3, 4) and (-2, -6)

m = (-6 - 4) / (-2 - (-3)) = (-10) / (1) = -10

Use point (-3, 4):
4 = -10*(-3) + b → 4 = 30 + b
b = 4 - 30 = -26

✔ Equation: y = -10x - 26

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## Problem 5: (-1, 2) and (0, -1)

m = (-1 - 2) / (0 - (-1)) = (-3) / (1) = -3

Point (0, -1) → so b = -1

✔ Equation: y = -3x - 1

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## Problem 6: (0, 1) and (1, 1)

m = (1 - 1) / (1 - 0) = 0 / 1 = 0

So it’s a horizontal line. Use point (0,1) → b = 1

✔ Equation: y = 0x + 1 → or just y = 1

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## Problem 7: (-3, 1) and (0, -3)

m = (-3 - 1) / (0 - (-3)) = (-4) / (3) = -4/3

Point (0, -3) → so b = -3

✔ Equation: y = -4/3 x - 3

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## Problem 8: (6, -3) and (-2, 3) ← Same as Problem 2!

We already solved this — same points.

✔ Equation: y = -3/4 x + 3/2

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Final Answer:

1. y = -3/2 x + 5
2. y = -3/4 x + 3/2
3. y = 7/5 x + 19/5
4. y = -10x - 26
5. y = -3x - 1
6. y = 1
7. y = -4/3 x - 3
8. y = -3/4 x + 3/2