Linear Equation from Two Points worksheet with coordinate grids and point pairs.

Let’s solve each problem step by step. We’ll find the equation of the line that passes through two given points. The general form we want is:

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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Problem 1: Points A(-6, -6) and B(6, -4)

Step 1: Find the slope (m)

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

Let’s use:
- Point A: x₁ = -6, y₁ = -6
- Point B: x₂ = 6, y₂ = -4

So:
m = (-4 - (-6)) / (6 - (-6))
= (-4 + 6) / (6 + 6)
= 2 / 12
= 1/6

Step 2: Use point-slope to find b

We can plug into y = mx + b using one point — let’s use point B(6, -4):

-4 = (1/6)(6) + b
-4 = 1 + b
b = -5

✔ So the equation is: y = (1/6)x - 5

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Problem 2: Points A(-3, -1) and B(-1, 3)

Step 1: Find the slope

x₁ = -3, y₁ = -1
x₂ = -1, y₂ = 3

m = (3 - (-1)) / (-1 - (-3))
= (3 + 1) / (-1 + 3)
= 4 / 2
= 2

Step 2: Find b

Use point B(-1, 3):

3 = 2*(-1) + b
3 = -2 + b
b = 5

✔ Equation: y = 2x + 5

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Problem 3: Points A(4, 8) and B(-4, 4)

Step 1: Slope

x₁ = 4, y₁ = 8
x₂ = -4, y₂ = 4

m = (4 - 8) / (-4 - 4)
= (-4) / (-8)
= 1/2

Step 2: Find b

Use point A(4, 8):

8 = (1/2)(4) + b
8 = 2 + b
b = 6

✔ Equation: y = (1/2)x + 6

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Problem 4: Points A(-8, 6) and B(2, -9)

Step 1: Slope

x₁ = -8, y₁ = 6
x₂ = 2, y₂ = -9

m = (-9 - 6) / (2 - (-8))
= (-15) / (10)
= -3/2

Step 2: Find b

Use point B(2, -9):

-9 = (-3/2)(2) + b
-9 = -3 + b
b = -6

✔ Equation: y = (-3/2)x - 6

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Final Answer:

1. y = (1/6)x - 5
2. y = 2x + 5
3. y = (1/2)x + 6
4. y = (-3/2)x - 6