To find the
slope of a line from its equation, we typically want to rewrite the equation in
slope-intercept form, which is:
>
y = mx + b
where:
-
m is the
slope
-
b is the y-intercept
So for each problem, we’ll solve for
y in terms of
x, then identify the coefficient of
x — that’s the slope.
---
1) 5x + 3y + 12 = 0
Solve for y:
→ 3y = -5x - 12
→ y = (-5/3)x - 4
✔ Slope = -5/3
---
2) 7x - 9 = y
This is already solved for y!
→ y = 7x - 9
✔ Slope = 7
---
3) -10 = 8x - y
Solve for y:
→ y = 8x + 10 *(add y to both sides and add 10 to both sides)*
✔ Slope = 8
---
4) 4y - 15 = -3x
Solve for y:
→ 4y = -3x + 15
→ y = (-3/4)x + 15/4
✔ Slope = -3/4
---
5) x = 3 + 7y
Solve for y:
→ x - 3 = 7y
→ y = (1/7)x - 3/7
✔ Slope = 1/7
---
6) 6x + 2y = -1
Solve for y:
→ 2y = -6x - 1
→ y = -3x - 1/2
✔ Slope = -3
---
7) 10x + 2y = -9
Solve for y:
→ 2y = -10x - 9
→ y = -5x - 9/2
✔ Slope = -5
---
8) 5y - 8x + 16 = 0
Solve for y:
→ 5y = 8x - 16
→ y = (8/5)x - 16/5
✔ Slope = 8/5
---
9) 5x = -6y + 9
Solve for y:
→ 6y = -5x + 9
→ y = (-5/6)x + 9/6 → simplify: y = (-5/6)x + 3/2
✔ Slope = -5/6
---
##
✔ Final Answers:
1)
-5/3
2)
7
3)
8
4)
-3/4
5)
1/7
6)
-3
7)
-5
8)
8/5
9)
-5/6
---
📌
Tip: Always isolate
y on one side. The number multiplying
x is your slope! If you end up with
x = constant, that’s a vertical line — undefined slope. But none of these are vertical.
Let me know if you’d like to graph any of them or verify with points!
Parent Tip: Review the logic above to help your child master the concept of find the slope and y intercept for each equation worksheet.
