Let’s solve each equation step by step to put them in
slope-intercept form, which is:
>
y = mx + b
Where:
-
m is the slope
-
b is the y-intercept
We’ll rearrange each equation so that
y is alone on one side.
---
1) 3x + 4y = 8
Subtract 3x from both sides:
→ 4y = -3x + 8
Divide everything by 4:
→ y = (-3/4)x + 2
✔ Final:
y = -¾x + 2
---
2) 9x + 35 = -5y
We want y alone. First, divide both sides by -5:
→ y = (9x)/(-5) + 35/(-5)
→ y = -9/5 x - 7
✔ Final:
y = -⁹₅x - 7
---
3) 2y - 6 = -6x
Add 6 to both sides:
→ 2y = -6x + 6
Divide by 2:
→ y = -3x + 3
✔ Final:
y = -3x + 3
---
4) -11x - 7y = -56
Add 11x to both sides:
→ -7y = 11x - 56
Divide by -7:
→ y = (11/-7)x + (-56/-7)
→ y = -11/7 x + 8
✔ Final:
y = -¹¹⁄₇x + 8
---
5) (5/3)y = -(x - 5)
First, simplify right side:
→ (5/3)y = -x + 5
Multiply both sides by 3 to eliminate denominator:
→ 5y = -3x + 15
Divide by 5:
→ y = (-3/5)x + 3
✔ Final:
y = -³⁄₅x + 3
---
6) -2(2x + y) = 28
Distribute the -2:
→ -4x - 2y = 28
Add 4x to both sides:
→ -2y = 4x + 28
Divide by -2:
→ y = -2x - 14
✔ Final:
y = -2x - 14
---
7) -14x + y = 7
Just add 14x to both sides:
→ y = 14x + 7
✔ Final:
y = 14x + 7
---
8) 12y = (8x - 48)/3
Simplify right side first:
→ 12y = (8/3)x - 16
Now divide both sides by 12:
→ y = (8/3)/12 x - 16/12
→ y = (8/(3×12))x - 4/3
→ y = (8/36)x - 4/3
→ Simplify 8/36 → 2/9
✔ Final:
y = ²⁄₉x - ⁴⁄₃
---
9) [3(x - y)] / 2 = 9
Multiply both sides by 2:
→ 3(x - y) = 18
Divide both sides by 3:
→ x - y = 6
Subtract x from both sides:
→ -y = -x + 6
Multiply both sides by -1:
→ y = x - 6
✔ Final:
y = x - 6
---
10) (2/3)x + 4(y - 2) = 0
First, distribute the 4:
→ (2/3)x + 4y - 8 = 0
Add 8 to both sides:
→ (2/3)x + 4y = 8
Subtract (2/3)x:
→ 4y = -(2/3)x + 8
Divide by 4:
→ y = [-(2/3)/4]x + 8/4
→ y = (-2/12)x + 2
→ Simplify -2/12 → -1/6
✔ Final:
y = -¹⁄₆x + 2
---
Final Answer:
1) y = -¾x + 2
2) y = -⁹⁄₅x - 7
3) y = -3x + 3
4) y = -¹¹⁄₇x + 8
5) y = -³⁄₅x + 3
6) y = -2x - 14
7) y = 14x + 7
8) y = ²⁄₉x - ⁴⁄₃
9) y = x - 6
10) y = -¹⁄₆x + 2
Parent Tip: Review the logic above to help your child master the concept of standard form to slope intercept form worksheet.
