To find the
slope from a linear equation, we typically convert the equation into
slope-intercept form, which is:
>
y = mx + b
where:
-
m is the
slope
-
b is the y-intercept
We’ll solve each problem by rearranging the equation to isolate
y and then identify the coefficient of
x, which is 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
Already in slope-intercept form: 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) Find the slope of the line whose equation is 5x = -6y + 9
Solve for y:
→ 6y = -5x + 9 *(Move terms: add 6y to both sides, subtract 9)*
→ y = (-5/6)x + 9/6
→ 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 remember —
slope is the coefficient of x when the equation is written as
y = mx + b. If the equation isn’t solved for y, rearrange it algebraically until it is!
Let me know if you’d like to see graphs or step-by-step visuals for any of these!
Parent Tip: Review the logic above to help your child master the concept of finding slope from an equation worksheet.
