Converting Between Standard and Slope-Intercept Forms (A) - Free Printable

Let’s solve each problem one by one. We’re converting between standard form (Ax + By = C) and slope-intercept form (y = mx + b).

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Problem 1:

Given: Slope-intercept form → y = -4x - 3
We need to write it in standard form.

Step: Move all terms to one side so that x and y are on the left, constant on right.

Add 4x to both sides:
→ 4x + y = -3

✔ Standard form: 4x + y = -3

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Problem 2:

Given: Standard form → x - 7y = 9
Solve for y to get slope-intercept form.

Step 1: Subtract x from both sides:
→ -7y = -x + 9

Step 2: Divide every term by -7:
→ y = (-x)/(-7) + 9/(-7)
→ y = (1/7)x - 9/7

✔ Slope-intercept form: y = (1/7)x - 9/7

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Problem 3:

Given: Standard form → x - 4y = -1
Solve for y.

Step 1: Subtract x from both sides:
→ -4y = -x - 1

Step 2: Divide by -4:
→ y = (-x)/(-4) + (-1)/(-4)
→ y = (1/4)x + 1/4

✔ Slope-intercept form: y = (1/4)x + 1/4

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Problem 4:

Given: Standard form → 5x + y = 6
Solve for y.

Subtract 5x from both sides:
→ y = -5x + 6

✔ Slope-intercept form: y = -5x + 6

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Problem 5:

Given: Slope-intercept form → y = -(10/7)x + 3/7
Convert to standard form.

Multiply every term by 7 to eliminate denominators:
→ 7y = -10x + 3

Add 10x to both sides:
→ 10x + 7y = 3

✔ Standard form: 10x + 7y = 3

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Problem 6:

Given: Standard form → 5x - 7y = -5
Solve for y.

Step 1: Subtract 5x from both sides:
→ -7y = -5x - 5

Step 2: Divide by -7:
→ y = (-5x)/(-7) + (-5)/(-7)
→ y = (5/7)x + 5/7

✔ Slope-intercept form: y = (5/7)x + 5/7

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Problem 7:

Given: Slope-intercept form → y = -(5/6)x - 5/6
Convert to standard form.

Multiply every term by 6:
→ 6y = -5x - 5

Add 5x to both sides:
→ 5x + 6y = -5

✔ Standard form: 5x + 6y = -5

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Problem 8:

Given: Slope-intercept form → y = -x - 10/11
Convert to standard form.

Multiply every term by 11:
→ 11y = -11x - 10

Add 11x to both sides:
→ 11x + 11y = -10

✔ Standard form: 11x + 11y = -10

*(Note: You could also leave it as is — no common factor to simplify further.)*

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Problem 9:

Given: Slope-intercept form → y = (5/3)x + 11/6
Convert to standard form.

Find LCD of denominators 3 and 6 → which is 6.

Multiply every term by 6:
→ 6y = 10x + 11

Subtract 10x from both sides:
→ -10x + 6y = 11

Usually we want A (coefficient of x) positive, so multiply entire equation by -1:
→ 10x - 6y = -11

✔ Standard form: 10x - 6y = -11

*(Alternatively, you can leave it as -10x + 6y = 11 — but conventionally, A should be positive if possible.)*

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Problem 10:

Given: Standard form → 5x - y = 1
Solve for y.

Subtract 5x from both sides:
→ -y = -5x + 1

Multiply both sides by -1:
→ y = 5x - 1

✔ Slope-intercept form: y = 5x - 1

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Final Answer:

1. Standard form: 4x + y = -3
2. Slope-intercept form: y = (1/7)x - 9/7
3. Slope-intercept form: y = (1/4)x + 1/4
4. Slope-intercept form: y = -5x + 6
5. Standard form: 10x + 7y = 3
6. Slope-intercept form: y = (5/7)x + 5/7
7. Standard form: 5x + 6y = -5
8. Standard form: 11x + 11y = -10
9. Standard form: 10x - 6y = -11
10. Slope-intercept form: y = 5x - 1