To find the slope and y-intercept from each graph, we use two key ideas:
- The
y-intercept is where the line crosses the y-axis (when x = 0). Look for the point on the vertical axis.
- The
slope tells us how steep the line is. It’s calculated as “rise over run” — how much the line goes up or down divided by how much it goes left or right between two points.
We’ll go one graph at a time.
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Graph 1:
Look at the line. It crosses the y-axis at y = 3 → so y-intercept = 3.
Pick two points on the line: (0, 3) and (-4, 0).
From (0, 3) to (-4, 0):
Down 3 units (rise = -3), left 4 units (run = -4).
Slope = rise/run = (-3)/(-4) = 3/4.
✔ Slope = 3/4, y-intercept = 3
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Graph 2:
Line crosses y-axis at y = 2 → y-intercept = 2.
Pick two points: (0, 2) and (5, 0).
From (0, 2) to (5, 0):
Down 2 (rise = -2), right 5 (run = 5).
Slope = -2/5.
✔ Slope = -2/5, y-intercept = 2
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Graph 3:
Line crosses y-axis at y = -4 → y-intercept = -4.
Pick two points: (0, -4) and (2, 0).
From (0, -4) to (2, 0):
Up 4 (rise = 4), right 2 (run = 2).
Slope = 4/2 = 2.
✔ Slope = 2, y-intercept = -4
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Graph 4:
Line crosses y-axis at y = 1 → y-intercept = 1.
Pick two points: (0, 1) and (-2, 4).
From (0, 1) to (-2, 4):
Up 3 (rise = 3), left 2 (run = -2).
Slope = 3 / (-2) = -3/2.
✔ Slope = -3/2, y-intercept = 1
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Graph 5:
Line crosses y-axis at y = -1 → y-intercept = -1.
Pick two points: (0, -1) and (2, 2).
From (0, -1) to (2, 2):
Up 3 (rise = 3), right 2 (run = 2).
Slope = 3/2.
✔ Slope = 3/2, y-intercept = -1
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Graph 6:
Line crosses y-axis at y = 0 → y-intercept = 0.
Pick two points: (0, 0) and (2, 4).
From (0, 0) to (2, 4):
Up 4 (rise = 4), right 2 (run = 2).
Slope = 4/2 = 2.
✔ Slope = 2, y-intercept = 0
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Final Answer:
1. Slope: 3/4, y-intercept: 3
2. Slope: -2/5, y-intercept: 2
3. Slope: 2, y-intercept: -4
4. Slope: -3/2, y-intercept: 1
5. Slope: 3/2, y-intercept: -1
6. Slope: 2, y-intercept: 0
Parent Tip: Review the logic above to help your child master the concept of find the slope and y intercept worksheet.
