Let’s solve each equation one by one. We need to convert them 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. Equation: -2x + y = -4
We want to get y alone on one side.
Add 2x to both sides:
→ y = 2x - 4
✔ Done. Slope-intercept form:
y = 2x - 4
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2. Equation: x + 3y = 3
Subtract x from both sides:
→ 3y = -x + 3
Now divide every term by 3:
→ y = (-1/3)x + 1
✔ Done. Slope-intercept form:
y = -⅓x + 1
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3. Equation: 5x + 6y = -12
Subtract 5x from both sides:
→ 6y = -5x - 12
Divide every term by 6:
→ y = (-5/6)x - 2
✔ Done. Slope-intercept form:
y = -⁵₆x - 2
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4. Equation: 4x + 3y = 3
Subtract 4x from both sides:
→ 3y = -4x + 3
Divide every term by 3:
→ y = (-4/3)x + 1
✔ Done. Slope-intercept form:
y = -⁴⁄x + 1
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5. Equation: 3x + y = -12
Subtract 3x from both sides:
→ y = -3x - 12
✔ Done. Slope-intercept form:
y = -3x - 12
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6. Equation: 4x + 7y = -14
Subtract 4x from both sides:
→ 7y = -4x - 14
Divide every term by 7:
→ y = (-4/7)x - 2
✔ Done. Slope-intercept form:
y = -⁴⁄₇x - 2
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Final Answer:
- -2x + y = -4 → y = 2x - 4
- x + 3y = 3 → y = -⅓x + 1
- 5x + 6y = -12 → y = -⁵⁄x - 2
- 4x + 3y = 3 → y = -⁴⁄₃x + 1
- 3x + y = -12 → y = -3x - 12
- 4x + 7y = -14 → y = -⁴⁄₇x - 2
Parent Tip: Review the logic above to help your child master the concept of slope y intercept worksheet.
