To find the
slope of a line from its equation, we need to rewrite the equation in
slope-intercept form, which is:
>
y = mx + b
where:
-
m is the
slope
-
b is the y-intercept
We’ll solve each problem by isolating
y on one side and identifying the coefficient of
x — that’s the slope.
---
1) 5x + 3y + 12 = 0
Step 1: Subtract 5x and 12 from both sides:
> 3y = -5x - 12
Step 2: Divide everything by 3:
> 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
Step 1: Add y to both sides:
> y - 10 = 8x
Step 2: Add 10 to both sides:
> y = 8x + 10
✔ Slope = 8
---
4) 4y - 15 = -3x
Step 1: Add 15 to both sides:
> 4y = -3x + 15
Step 2: Divide by 4:
> y = (-3/4)x + 15/4
✔ Slope = -3/4
---
5) x = 3 + 7y
Step 1: Subtract 3 from both sides:
> x - 3 = 7y
Step 2: Divide by 7:
> y = (1/7)x - 3/7
✔ Slope = 1/7
---
6) 6x + 2y = -1
Step 1: Subtract 6x from both sides:
> 2y = -6x - 1
Step 2: Divide by 2:
> y = -3x - 1/2
✔ Slope = -3
---
7) 10x + 2y = -9
Step 1: Subtract 10x from both sides:
> 2y = -10x - 9
Step 2: Divide by 2:
> y = -5x - 9/2
✔ Slope = -5
---
8) 5y - 8x + 16 = 0
Step 1: Add 8x and subtract 16 from both sides:
> 5y = 8x - 16
Step 2: Divide by 5:
> y = (8/5)x - 16/5
✔ Slope = 8/5
---
9) 5x = -6y + 9
Step 1: Add 6y to both sides:
> 5x + 6y = 9
Step 2: Subtract 5x from both sides:
> 6y = -5x + 9
Step 3: Divide by 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
Let me know if you’d like to graph any of these or understand why slope matters!
Parent Tip: Review the logic above to help your child master the concept of slope equation worksheet.
