Of course! Let's solve this worksheet step by step.
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## 📘
What is Standard Form?
The
standard form of a linear equation is:
>
Ax + By = C
Where:
- A, B, and C are integers (no fractions or decimals),
- A should be non-negative (A ≥ 0),
- A, B, and C have no common factors other than 1 (i.e., the equation is simplified).
We’ll convert each given equation from
slope-intercept form (y = mx + b) to
standard form (Ax + By = C).
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#
✔ PART 1: Convert from slope-intercept form to standard form
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① y = -2x + 1
Step 1: Move all terms to one side to get x and y on the left.
Add 2x to both sides:
> 2x + y = 1
✔ Already in standard form. A=2, B=1, C=1 — all integers, A > 0.
Answer: 2x + y = 1
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② y = -3x + 2
Step 1: Add 3x to both sides:
> 3x + y = 2
✔ Standard form.
Answer: 3x + y = 2
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③ y = (1/4)x + 3/4
Fractions! We need to eliminate them.
Step 1: Multiply every term by 4 (LCM of denominators):
> 4y = x + 3
Step 2: Move x to the left:
> -x + 4y = 3
Step 3: Make A positive (multiply both sides by -1):
> x - 4y = -3
✔ Standard form.
Answer: x - 4y = -3
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④ y = (2/7)x + 1/7
Multiply every term by 7 to eliminate denominators:
> 7y = 2x + 1
Move 2x to the left:
> -2x + 7y = 1
Make A positive (multiply by -1):
> 2x - 7y = -1
✔ Standard form.
Answer: 2x - 7y = -1
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⑤ y = -6x - 2
Add 6x to both sides:
> 6x + y = -2
✔ Already in standard form.
Answer: 6x + y = -2
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⑥ y = (-1/6)x - 5/6
Multiply every term by 6:
> 6y = -x - 5
Move -x to the left:
> x + 6y = -5
✔ Standard form.
Answer: x + 6y = -5
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#
✔ PART 2: Use slope and y-intercept to write equations in standard form
First, write the equation in
slope-intercept form (y = mx + b), then convert to standard form.
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① Slope = -8, y-intercept = 5
Slope-intercept form:
> y = -8x + 5
Convert to standard form:
Add 8x to both sides:
> 8x + y = 5
✔ Standard form.
Answer: 8x + y = 5
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② Slope = 5/2, y-intercept = 1
Slope-intercept form:
> y = (5/2)x + 1
Multiply every term by 2 to eliminate fraction:
> 2y = 5x + 2
Move 5x to the left:
> -5x + 2y = 2
Make A positive (multiply by -1):
> 5x - 2y = -2
✔ Standard form.
Answer: 5x - 2y = -2
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③ Slope = 7/2, y-intercept = 3
Slope-intercept form:
> y = (7/2)x + 3
Multiply every term by 2:
> 2y = 7x + 6
Move 7x to the left:
> -7x + 2y = 6
Multiply by -1:
> 7x - 2y = -6
✔ Standard form.
Answer: 7x - 2y = -6
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④ Slope = 3/5, y-intercept = 1
Slope-intercept form:
> y = (3/5)x + 1
Multiply every term by 5:
> 5y = 3x + 5
Move 3x to the left:
> -3x + 5y = 5
Multiply by -1:
> 3x - 5y = -5
✔ Standard form.
Answer: 3x - 5y = -5
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# 📝 Final Answers Summary:
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##
✔ Part 1: Convert from slope-intercept form
1.
2x + y = 1
2.
3x + y = 2
3.
x - 4y = -3
4.
2x - 7y = -1
5.
6x + y = -2
6.
x + 6y = -5
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##
✔ Part 2: Write using slope and y-intercept
1.
8x + y = 5
2.
5x - 2y = -2
3.
7x - 2y = -6
4.
3x - 5y = -5
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Parent Tip: Review the logic above to help your child master the concept of linear equations standard form worksheet.
