You’ve uploaded a worksheet titled
“Finding Slopes From an Equation”. The task is to find the
slope of each line given its equation.
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## 📌 Key Concept:
The
slope of a line is usually denoted by
`m`. To find it from an equation, we typically convert the equation into
Slope-Intercept Form:
>
y = mx + b
Where:
- `m` = slope
- `b` = y-intercept
If the equation is already in this form, the coefficient of `x` is the slope.
If not, we solve for `y` to get it into that form.
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Let’s go through each problem one by one.
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✔ 1) y = (1/2)x - 5
Already in slope-intercept form:
→
Slope = 1/2
---
✔ 2) y = - (4/5)x + 3
Already in slope-intercept form:
→
Slope = -4/5
---
✔ 3) y = -x + 6
This is the same as: y = -1x + 6
→
Slope = -1
---
✔ 4) y = -4x - 1
Already in slope-intercept form:
→
Slope = -4
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✔ 5) 2x - y = 8
We need to solve for `y`.
Subtract 2x from both sides:
→ -y = -2x + 8
Multiply both sides by -1:
→ y = 2x - 8
→
Slope = 2
---
✔ 6) x + 2y = -8
Solve for `y`.
Subtract `x` from both sides:
→ 2y = -x - 8
Divide everything by 2:
→ y = (-1/2)x - 4
→
Slope = -1/2
---
✔ 7) 4x + 2y = 0
Solve for `y`.
Subtract 4x:
→ 2y = -4x
Divide by 2:
→ y = -2x + 0 → y = -2x
→
Slope = -2
---
✔ 8) 4x + 2y = -10
Solve for `y`.
Subtract 4x:
→ 2y = -4x - 10
Divide by 2:
→ y = -2x - 5
→
Slope = -2
---
✔ 9) x - y = -2
Solve for `y`.
Subtract `x`:
→ -y = -x - 2
Multiply by -1:
→ y = x + 2
→
Slope = 1
---
✔ 10) 8x - 2y = 0
Solve for `y`.
Subtract 8x:
→ -2y = -8x
Divide by -2:
→ y = 4x
→
Slope = 4
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##
✔ Final Answers:
| Problem | Slope |
|---------|-----------|
| 1 | 1/2 |
| 2 | -4/5 |
| 3 | -1 |
| 4 | -4 |
| 5 | 2 |
| 6 | -1/2 |
| 7 | -2 |
| 8 | -2 |
| 9 | 1 |
| 10 | 4 |
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## 💡 Tip:
Always remember — if you’re not sure,
solve for y and look at the coefficient of `x`. That’s your slope!
Let me know if you want to check your work or need help graphing these lines too! 😊
Parent Tip: Review the logic above to help your child master the concept of slope equation worksheet.
