Sure! Let’s solve each problem step by step.
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The goal is to find the
slope and
y-intercept for each linear equation.
All these equations are in
slope-intercept form, which is:
>
y = mx + b
Where:
-
m = slope
-
b = y-intercept (the point where the line crosses the y-axis, i.e., when x = 0)
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Let’s go one by one:
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1) y = -5x - 3
- Slope (m) =
-5
- y-intercept (b) =
-3
✔ Answer:
Slope =
-5
y-intercept =
-3
---
2) y = ½x + 4
- Slope (m) =
½
- y-intercept (b) =
4
✔ Answer:
Slope =
½
y-intercept =
4
---
3) y = ⅔x - 1
- Slope (m) =
⅔
- y-intercept (b) =
-1
✔ Answer:
Slope =
⅔
y-intercept =
-1
---
4) y = -2x + 2
- Slope (m) =
-2
- y-intercept (b) =
2
✔ Answer:
Slope =
-2
y-intercept =
2
---
5) y = ¼x - 5
- Slope (m) =
¼
- y-intercept (b) =
-5
✔ Answer:
Slope =
¼
y-intercept =
-5
---
6) y = ½x + 4
*(Same as #2)*
- Slope (m) =
½
- y-intercept (b) =
4
✔ Answer:
Slope =
½
y-intercept =
4
---
7) y = ¼x + 4
- Slope (m) =
¼
- y-intercept (b) =
4
✔ Answer:
Slope =
¼
y-intercept =
4
---
8) y = 3x + 2
- Slope (m) =
3
- y-intercept (b) =
2
✔ Answer:
Slope =
3
y-intercept =
2
---
9) y = -⁵⁄₄x - 2
- Slope (m) =
-⁵⁄₄
- y-intercept (b) =
-2
✔ Answer:
Slope =
-⁵⁄₄
y-intercept =
-2
---
10) y = ³⁄₂x + 1
- Slope (m) =
³⁄₂
- y-intercept (b) =
1
✔ Answer:
Slope =
³⁄₂
y-intercept =
1
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✔ Final Answers Summary:
| Problem | Slope | y-intercept |
|---------|-----------|-------------|
| 1 | -5 | -3 |
| 2 | ½ | 4 |
| 3 | ⅔ | -1 |
| 4 | -2 | 2 |
| 5 | ¼ | -5 |
| 6 | ½ | 4 |
| 7 | ¼ | 4 |
| 8 | 3 | 2 |
| 9 | -⁵⁄₄ | -2 |
| 10 | ³⁄₂ | 1 |
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📌
Tip: Always look for the coefficient of
x — that’s your slope. The constant term (with no x) is your y-intercept!
Let me know if you’d like a graph or explanation of how to plot any of these lines!
Parent Tip: Review the logic above to help your child master the concept of find the slope and y intercept for each equation worksheet.
