Let's solve each problem step-by-step on the
Slope-Intercept Form Worksheet. The
slope-intercept form of a line is:
$$
y = mx + b
$$
where:
- $ m $ is the
slope
- $ b $ is the
y-intercept
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Part 1: Write each equation in slope-intercept form (solve for $ y $)
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####
1. $ 2x + 4y = 8 $
We want to solve for $ y $:
$$
4y = -2x + 8
$$
Divide both sides by 4:
$$
y = -\frac{1}{2}x + 2
$$
✔ Answer: $ y = -\frac{1}{2}x + 2 $
---
####
2. $ 4 - 8x = 2y $
Start by isolating $ y $:
$$
2y = -8x + 4
$$
Divide by 2:
$$
y = -4x + 2
$$
✔ Answer: $ y = -4x + 2 $
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####
3. $ -12x + y = 8 $
Solve for $ y $:
$$
y = 12x + 8
$$
✔ Answer: $ y = 12x + 8 $
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####
4. $ 2y - 6 = -6x $
Add 6 to both sides:
$$
2y = -6x + 6
$$
Divide by 2:
$$
y = -3x + 3
$$
✔ Answer: $ y = -3x + 3 $
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####
5. $ 7 = 2x - y $
Rewriting:
$$
-y = -2x + 7
$$
Multiply both sides by -1:
$$
y = 2x - 7
$$
✔ Answer: $ y = 2x - 7 $
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####
6. $ 4y = 4x $
Divide both sides by 4:
$$
y = x
$$
✔ Answer: $ y = x $
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Part 2: Write the slope-intercept form given slope and y-intercept
Use: $ y = mx + b $
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####
7. Slope = 3, y-intercept = -2
$$
y = 3x - 2
$$
✔ Answer: $ y = 3x - 2 $
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####
8. Slope = -3, y-intercept = 7
$$
y = -3x + 7
$$
✔ Answer: $ y = -3x + 7 $
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####
9. Slope = 0, y-intercept = -1
A horizontal line with zero slope:
$$
y = 0x - 1 \Rightarrow y = -1
$$
✔ Answer: $ y = -1 $
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####
10. Slope = $-\frac{1}{2}$, y-intercept = -2
$$
y = -\frac{1}{2}x - 2
$$
✔ Answer: $ y = -\frac{1}{2}x - 2 $
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####
11. Slope = $-\frac{4}{5}$, y-intercept = 0
$$
y = -\frac{4}{5}x + 0 \Rightarrow y = -\frac{4}{5}x
$$
✔ Answer: $ y = -\frac{4}{5}x $
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####
12. Slope = -1, y-intercept = -4
$$
y = -x - 4
$$
✔ Answer: $ y = -x - 4 $
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✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | $ y = -\frac{1}{2}x + 2 $ |
| 2 | $ y = -4x + 2 $ |
| 3 | $ y = 12x + 8 $ |
| 4 | $ y = -3x + 3 $ |
| 5 | $ y = 2x - 7 $ |
| 6 | $ y = x $ |
| 7 | $ y = 3x - 2 $ |
| 8 | $ y = -3x + 7 $ |
| 9 | $ y = -1 $ |
| 10 | $ y = -\frac{1}{2}x - 2 $ |
| 11 | $ y = -\frac{4}{5}x $ |
| 12 | $ y = -x - 4 $ |
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Let me know if you'd like this formatted as a printable worksheet or need explanations for any specific step!
Parent Tip: Review the logic above to help your child master the concept of slope intercept worksheet with answers.
