Absolutely! Let’s solve each of the 6 problems step by step. The goal is to find the
slope (m) and the
y-intercept (b) for each line graphed, then write the equation in
slope-intercept form: `y = mx + b`.
---
## 🔢 Key Concepts:
-
Slope (m) = rise / run = `(change in y) / (change in x)` = `(y₂ - y₁) / (x₂ - x₁)`
-
y-intercept (b) = the y-value where the line crosses the y-axis (i.e., when `x = 0`)
- Once you have `m` and `b`, plug them into `y = mx + b`
---
# 📈 Problem 1
Graph: Line goes from top-left to bottom-right → negative slope.
Pick two clear points:
- Point A: (0, 4) ← this is the y-intercept!
- Point B: (2, 0)
→ Slope `m = (0 - 4) / (2 - 0) = (-4)/2 = -2`
→ y-intercept `b = 4` (since it crosses y-axis at (0,4))
✔ Equation: `y = -2x + 4`
---
# 📈 Problem 2
Graph: Line goes from bottom-left to top-right → positive slope.
Pick two points:
- Point A: (0, -3) ← y-intercept
- Point B: (2, 1)
→ Slope `m = (1 - (-3)) / (2 - 0) = (4)/2 = 2`
→ y-intercept `b = -3`
✔ Equation: `y = 2x - 3`
---
# 📈 Problem 3
Graph: Line goes from top-left to bottom-right → negative slope.
Pick two points:
- Point A: (0, -1) ← y-intercept
- Point B: (3, -3)
→ Slope `m = (-3 - (-1)) / (3 - 0) = (-2)/3`
→ y-intercept `b = -1`
✔ Equation: `y = (-2/3)x - 1`
---
# 📈 Problem 4
Graph: Line goes from bottom-left to top-right → positive slope.
Pick two points:
- Point A: (0, 1) ← y-intercept
- Point B: (1, 4)
→ Slope `m = (4 - 1) / (1 - 0) = 3/1 = 3`
→ y-intercept `b = 1`
✔ Equation: `y = 3x + 1`
---
# 📈 Problem 5
Graph: Line goes from top-left to bottom-right → negative slope.
Pick two points:
- Point A: (0, -4) ← y-intercept
- Point B: (2, -8)
→ Slope `m = (-8 - (-4)) / (2 - 0) = (-4)/2 = -2`
→ y-intercept `b = -4`
✔ Equation: `y = -2x - 4`
---
# 📈 Problem 6
Graph: Line goes from bottom-left to top-right → positive slope.
Pick two points:
- Point A: (0, 1) ← y-intercept
- Point B: (3, 3)
→ Slope `m = (3 - 1) / (3 - 0) = 2/3`
→ y-intercept `b = 1`
✔ Equation: `y = (2/3)x + 1`
---
##
✔ Final Answers Summary:
| Problem | Slope (m) | y-intercept (b) | Equation |
|---------|------------------|------------------|-----------------------|
| 1 | -2 | 4 | `y = -2x + 4` |
| 2 | 2 | -3 | `y = 2x - 3` |
| 3 | -2/3 | -1 | `y = (-2/3)x - 1` |
| 4 | 3 | 1 | `y = 3x + 1` |
| 5 | -2 | -4 | `y = -2x - 4` |
| 6 | 2/3 | 1 | `y = (2/3)x + 1` |
---
Let me know if you’d like a visual explanation or how to check your answers using another point on the line! 😊
Parent Tip: Review the logic above to help your child master the concept of equations of a line worksheet.
