Sure! Let’s solve each problem step-by-step. The goal is to convert each linear equation from
standard form (Ax + By = C) to
slope-intercept form (y = mx + b), where
m is the slope and
b is the y-intercept.
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1. 10x + 9y = -20
We want to isolate
y.
Step 1: Subtract 10x from both sides:
> 9y = -10x - 20
Step 2: Divide every term by 9:
> y = (-10/9)x - 20/9
✔ Answer: y = -10/9 x - 20/9
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2. -9x + 16y = -8
Isolate
y.
Step 1: Add 9x to both sides:
> 16y = 9x - 8
Step 2: Divide every term by 16:
> y = (9/16)x - 8/16
Simplify -8/16 → -1/2
✔ Answer: y = 9/16 x - 1/2
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3. -x - 4y = 9
Isolate
y.
Step 1: Add x to both sides:
> -4y = x + 9
Step 2: Divide every term by -4:
> y = (-1/4)x - 9/4
✔ Answer: y = -1/4 x - 9/4
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4. 16x + 7y = -15
Isolate
y.
Step 1: Subtract 16x from both sides:
> 7y = -16x - 15
Step 2: Divide every term by 7:
> y = (-16/7)x - 15/7
✔ Answer: y = -16/7 x - 15/7
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5. 13x + y = 10
Isolate
y.
Step 1: Subtract 13x from both sides:
> y = -13x + 10
✔ Answer: y = -13x + 10
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6. (3/4)x + (1/3)y = -4
This one has fractions — let’s eliminate them first or isolate y directly.
Isolate
y:
Step 1: Subtract (3/4)x from both sides:
> (1/3)y = -(3/4)x - 4
Step 2: Multiply both sides by 3 to eliminate the fraction:
> y = 3 * [-(3/4)x - 4]
> y = -(9/4)x - 12
✔ Answer: y = -9/4 x - 12
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7. (3/4)x - (2/3)y = -1
Isolate
y.
Step 1: Subtract (3/4)x from both sides:
> -(2/3)y = -(3/4)x - 1
Step 2: Multiply both sides by -1:
> (2/3)y = (3/4)x + 1
Step 3: Multiply both sides by 3/2 to solve for y:
> y = (3/2) * [(3/4)x + 1]
> y = (9/8)x + 3/2
✔ Answer: y = 9/8 x + 3/2
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8. -(3/4)x + (3/5)y = 0
Isolate
y.
Step 1: Add (3/4)x to both sides:
> (3/5)y = (3/4)x
Step 2: Multiply both sides by 5/3:
> y = (5/3) * (3/4)x
> y = (15/12)x → simplify 15/12 to 5/4
✔ Answer: y = 5/4 x
*(Note: Since there’s no constant term, the y-intercept is 0.)*
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✔ Final Answers Summary:
1.
y = -10/9 x - 20/9
2.
y = 9/16 x - 1/2
3.
y = -1/4 x - 9/4
4.
y = -16/7 x - 15/7
5.
y = -13x + 10
6.
y = -9/4 x - 12
7.
y = 9/8 x + 3/2
8.
y = 5/4 x
Let me know if you’d like a graph or further explanation for any of these!
Parent Tip: Review the logic above to help your child master the concept of linear equations slope intercept form worksheet.
