Let’s solve each problem one by one. We’re looking for the
slope-intercept form of each line, which is:
>
y = mx + b
Where:
-
m = slope (rise over run)
-
b = y-intercept (where the line crosses the y-axis)
We’ll find two points on each line, calculate the slope, then plug in to find b.
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Problem 1)
Line goes through (0, -2) and (1, 2).
Slope m = (2 - (-2)) / (1 - 0) = 4/1 =
4
Y-intercept b = -2 (since it crosses at (0, -2))
→ Equation:
y = 4x - 2
---
Problem 2)
Line goes through (0, -1) and (4, -3).
Slope m = (-3 - (-1)) / (4 - 0) = (-2)/4 =
-1/2
Y-intercept b = -1
→ Equation:
y = -½x - 1
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Problem 3)
Line goes through (0, -3) and (4, -5).
Slope m = (-5 - (-3)) / (4 - 0) = (-2)/4 =
-1/2
Y-intercept b = -3
→ Equation:
y = -½x - 3
---
Problem 4)
Horizontal line at y = 2 → slope = 0
Equation:
y = 2
---
Problem 5)
Line goes through (0, 3) and (-4, -1).
Slope m = (-1 - 3) / (-4 - 0) = (-4)/(-4) =
1
Y-intercept b = 3
→ Equation:
y = x + 3
---
Problem 6)
Line goes through (0, -3) and (1, 1).
Slope m = (1 - (-3)) / (1 - 0) = 4/1 =
4
Y-intercept b = -3
→ Equation:
y = 4x - 3
---
Problem 7)
Line goes through (0, 3) and (-1, -1).
Slope m = (-1 - 3) / (-1 - 0) = (-4)/(-1) =
4
Y-intercept b = 3
→ Equation:
y = 4x + 3
---
Problem 8)
Line goes through (0, 3) and (-2, -1).
Slope m = (-1 - 3) / (-2 - 0) = (-4)/(-2) =
2
Y-intercept b = 3
→ Equation:
y = 2x + 3
---
Final Answer:
1) y = 4x - 2
2) y = -½x - 1
3) y = -½x - 3
4) y = 2
5) y = x + 3
6) y = 4x - 3
7) y = 4x + 3
8) y = 2x + 3
Parent Tip: Review the logic above to help your child master the concept of writing equations from graphs worksheet pdf.
