Let’s solve each part step by step.
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Part 1: Find slope and y-intercept from equations
We use the form:
y = mx + b
where
m = slope,
b = y-intercept
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Problem 1: y = 4x + 7
→ Already in slope-intercept form.
Slope (m) = 4
Y-intercept (b) = 7
✔ Slope: 4, Y-intercept: 7
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Problem 2: y = -2x
→ This is same as y = -2x + 0
Slope = -2
Y-intercept = 0
✔ Slope: -2, Y-intercept: 0
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Problem 3: y = x + 1
→ Same as y = 1x + 1
Slope = 1
Y-intercept = 1
✔ Slope: 1, Y-intercept: 1
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Problem 4: y = 5
→ This is a horizontal line. Can be written as y = 0x + 5
Slope = 0 (no rise, only run)
Y-intercept = 5
✔ Slope: 0, Y-intercept: 5
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Problem 5: y = ½x
→ Same as y = ½x + 0
Slope = ½
Y-intercept = 0
✔ Slope: ½, Y-intercept: 0
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Problem 6: y = -⅓x - 6
Already in slope-intercept form.
Slope = -⅓
Y-intercept = -6
✔ Slope: -⅓, Y-intercept: -6
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Problem 7: y = 3
Same as Problem 4 — horizontal line.
y = 0x + 3
Slope = 0
Y-intercept = 3
✔ Slope: 0, Y-intercept: 3
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Problem 8: y = -x - 5
Same as y = -1x - 5
Slope = -1
Y-intercept = -5
✔ Slope: -1, Y-intercept: -5
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Part 2: Graph the linear equation using intercepts and slope
We’ll find two points for each line to graph it. Usually easiest to use:
- Y-intercept (set x=0)
- X-intercept (set y=0), or use slope to find another point.
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Problem 9: y = 2x - 1
Y-intercept: when x=0 → y = -1 → Point: (0, -1)
Use slope = 2 = 2/1 → from (0,-1), go up 2, right 1 → (1, 1)
Plot (0, -1) and (1, 1), draw line.
✔ Points to plot: (0, -1), (1, 1)
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Problem 10: y = -x + 2
Y-intercept: x=0 → y=2 → (0, 2)
Slope = -1 = -1/1 → from (0,2), go down 1, right 1 → (1, 1)
Plot (0,2) and (1,1), draw line.
✔ Points to plot: (0, 2), (1, 1)
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Problem 11: y = x + 3
Y-intercept: x=0 → y=3 → (0, 3)
Slope = 1 → from (0,3), go up 1, right 1 → (1, 4)
Plot (0,3) and (1,4), draw line.
✔ Points to plot: (0, 3), (1, 4)
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Problem 12: y = -½x
Y-intercept: x=0 → y=0 → (0, 0)
Slope = -½ → from (0,0), go down 1, right 2 → (2, -1)
Plot (0,0) and (2,-1), draw line.
✔ Points to plot: (0, 0), (2, -1)
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Problem 13: y = ¼x - 3
Y-intercept: x=0 → y=-3 → (0, -3)
Slope = ¼ → from (0,-3), go up 1, right 4 → (4, -2)
Plot (0,-3) and (4,-2), draw line.
✔ Points to plot: (0, -3), (4, -2)
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Problem 14: y = ⅔x + 1
Y-intercept: x=0 → y=1 → (0, 1)
Slope = ⅔ → from (0,1), go up 2, right 3 → (3, 3)
Plot (0,1) and (3,3), draw line.
✔ Points to plot: (0, 1), (3, 3)
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Final Answer:
Part 1:
1. Slope: 4, Y-intercept: 7
2. Slope: -2, Y-intercept: 0
3. Slope: 1, Y-intercept: 1
4. Slope: 0, Y-intercept: 5
5. Slope: ½, Y-intercept: 0
6. Slope: -⅓, Y-intercept: -6
7. Slope: 0, Y-intercept: 3
8. Slope: -1, Y-intercept: -5
Part 2 (Points to graph):
9. (0, -1), (1, 1)
10. (0, 2), (1, 1)
11. (0, 3), (1, 4)
12. (0, 0), (2, -1)
13. (0, -3), (4, -2)
14. (0, 1), (3, 3)
Parent Tip: Review the logic above to help your child master the concept of hard algebra y mx b worksheet.
