Worksheet featuring four linear equations plotted on coordinate grids, showing slope, y-intercept, and equation for each line.

Let’s solve each problem one by one. For each graph, we need to find:

- Slope (how steep the line is — rise over run)
- y-intercept (where the line crosses the y-axis — that’s when x = 0)
- Equation in slope-intercept form: y = mx + b, where m = slope, b = y-intercept

We’ll go step by step for each number.

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Problem 7

Look at the line. Pick two clear points on the line.

From the graph:
- When x = 0, y = -6 → so y-intercept = -6
- Another point: when x = 2, y = -7? Wait — let’s check better.

Actually, looking carefully:

At x = 0 → y = -6
At x = 4 → y = -8? Let’s count grid squares.

Better: from (0, -6) to (4, -8):
Rise = -8 - (-6) = -2
Run = 4 - 0 = 4
Slope = rise/run = -2/4 = -1/2

Check another pair: from (0, -6) to (-4, -4):
Rise = -4 - (-6) = +2
Run = -4 - 0 = -4
Slope = 2 / -4 = -1/2 → same!

✔ Slope = -1/2
✔ y-intercept = -6
✔ Equation: y = (-1/2)x - 6

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Problem 8

Find two points.

Looks like it passes through (0, 3) → so y-intercept = 3

Another point: (4, 4)? Let’s see: from (0,3) to (4,4):

Rise = 4 - 3 = 1
Run = 4 - 0 = 4
Slope = 1/4

Check another: from (0,3) to (-4,2):
Rise = 2 - 3 = -1
Run = -4 - 0 = -4
Slope = (-1)/(-4) = 1/4 → good!

✔ Slope = 1/4
✔ y-intercept = 3
✔ Equation: y = (1/4)x + 3

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Problem 9

This line is very steep and going down.

It crosses y-axis at (0, 3) → y-intercept = 3

Now pick another point: looks like (1, -1)? Let’s check:

From (0,3) to (1,-1):
Rise = -1 - 3 = -4
Run = 1 - 0 = 1
Slope = -4/1 = -4

Check another: from (0,3) to (2, -5):
Rise = -5 - 3 = -8
Run = 2 - 0 = 2
Slope = -8/2 = -4 → yes!

✔ Slope = -4
✔ y-intercept = 3
✔ Equation: y = -4x + 3

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Problem 10

Line goes up to the right.

Crosses y-axis at (0, 2) → y-intercept = 2

Pick another point: (3, 4)? From (0,2) to (3,4):

Rise = 4 - 2 = 2
Run = 3 - 0 = 3
Slope = 2/3

Check: from (0,2) to (-3,0):
Rise = 0 - 2 = -2
Run = -3 - 0 = -3
Slope = (-2)/(-3) = 2/3 → correct!

✔ Slope = 2/3
✔ y-intercept = 2
✔ Equation: y = (2/3)x + 2

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Problem 11

Line goes down to the right.

Crosses y-axis at (0, 1) → y-intercept = 1

Pick another point: (4, -1)? From (0,1) to (4,-1):

Rise = -1 - 1 = -2
Run = 4 - 0 = 4
Slope = -2/4 = -1/2

Check: from (0,1) to (-4,3):
Rise = 3 - 1 = 2
Run = -4 - 0 = -4
Slope = 2/-4 = -1/2 → good!

✔ Slope = -1/2
✔ y-intercept = 1
✔ Equation: y = (-1/2)x + 1

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Problem 12

Line goes up to the right.

Crosses y-axis at (0, -3) → y-intercept = -3

Pick another point: (4, 0)? From (0,-3) to (4,0):

Rise = 0 - (-3) = 3
Run = 4 - 0 = 4
Slope = 3/4

Check: from (0,-3) to (-4,-6):
Rise = -6 - (-3) = -3
Run = -4 - 0 = -4
Slope = (-3)/(-4) = 3/4 → perfect!

✔ Slope = 3/4
✔ y-intercept = -3
✔ Equation: y = (3/4)x - 3

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Final Answer:

7. Slope: -1/2, y-intercept: -6, Equation: y = (-1/2)x - 6
8. Slope: 1/4, y-intercept: 3, Equation: y = (1/4)x + 3
9. Slope: -4, y-intercept: 3, Equation: y = -4x + 3
10. Slope: 2/3, y-intercept: 2, Equation: y = (2/3)x + 2
11. Slope: -1/2, y-intercept: 1, Equation: y = (-1/2)x + 1
12. Slope: 3/4, y-intercept: -3, Equation: y = (3/4)x - 3