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 to calculate slope, then use one point and the slope to find b — or just read b directly if the line crosses the y-axis at a grid point.
---
Problem 1)
Line goes through (0, -2) and (1, 1).
Slope m = (change in y)/(change in x) = (1 - (-2)) / (1 - 0) = 3/1 =
3
Y-intercept b = -2 (since it crosses y-axis at -2)
→ Equation:
y = 3x - 2
---
Problem 2)
Line goes through (0, 1) and (4, -1)
Slope m = (-1 - 1)/(4 - 0) = (-2)/4 =
-1/2
Y-intercept b = 1
→ Equation:
y = -½x + 1
---
Problem 3)
Line goes through (0, -2) and (-4, 0)
Slope m = (0 - (-2))/(-4 - 0) = 2 / (-4) =
-1/2
Y-intercept b = -2
→ Equation:
y = -½x - 2
---
Problem 4)
Horizontal line at y = 3 → slope = 0
Equation:
y = 3
(No x term because it never rises or falls.)
---
Problem 5)
Line goes through (0, 3) and (-4, 0)
Slope m = (0 - 3)/(-4 - 0) = (-3)/(-4) =
3/4
Y-intercept b = 3
→ Equation:
y = ¾x + 3
---
Problem 6)
Line goes through (0, -1) and (1, 2)
Slope m = (2 - (-1))/(1 - 0) = 3/1 =
3
Y-intercept b = -1
→ Equation:
y = 3x - 1
---
Problem 7)
Line goes through (0, 2) and (-1, -2)
Slope m = (-2 - 2)/(-1 - 0) = (-4)/(-1) =
4
Y-intercept b = 2
→ Equation:
y = 4x + 2
---
Problem 8)
Line goes through (0, 1) and (-2, -3)
Slope m = (-3 - 1)/(-2 - 0) = (-4)/(-2) =
2
Y-intercept b = 1
→ Equation:
y = 2x + 1
---
Final Answer:
1) y = 3x - 2
2) y = -½x + 1
3) y = -½x - 2
4) y = 3
5) y = ¾x + 3
6) y = 3x - 1
7) y = 4x + 2
8) y = 2x + 1
Parent Tip: Review the logic above to help your child master the concept of writing linear equations from graphs worksheet.
