Let's solve each problem step by step using the
slope formula:
The slope $ m $ of a line passing through two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is given by:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$
We'll apply this formula to each pair of points.
---
1. Points: (-1, -4), (3, -3)
$$
m = \frac{-3 - (-4)}{3 - (-1)} = \frac{-3 + 4}{3 + 1} = \frac{1}{4}
$$
✔ Slope = $ \frac{1}{4} $
---
2. Points: (1, -5), (-4, 5)
$$
m = \frac{5 - (-5)}{-4 - 1} = \frac{5 + 5}{-5} = \frac{10}{-5} = -2
$$
✔ Slope = $ -2 $
---
3. Points: (-5, -3), (5, -5)
$$
m = \frac{-5 - (-3)}{5 - (-5)} = \frac{-5 + 3}{5 + 5} = \frac{-2}{10} = -\frac{1}{5}
$$
✔ Slope = $ -\frac{1}{5} $
---
4. Points: (2, -5), (0, 5)
$$
m = \frac{5 - (-5)}{0 - 2} = \frac{5 + 5}{-2} = \frac{10}{-2} = -5
$$
✔ Slope = $ -5 $
---
5. Points: (-5, 0), (5, -2)
$$
m = \frac{-2 - 0}{5 - (-5)} = \frac{-2}{5 + 5} = \frac{-2}{10} = -\frac{1}{5}
$$
✔ Slope = $ -\frac{1}{5} $
---
6. Points: (-5, -4), (5, -1)
$$
m = \frac{-1 - (-4)}{5 - (-5)} = \frac{-1 + 4}{5 + 5} = \frac{3}{10}
$$
✔ Slope = $ \frac{3}{10} $
---
✔ Final Answers:
| Points | Slope |
|--------|-------|
| (-1, -4), (3, -3) | $ \frac{1}{4} $ |
| (1, -5), (-4, 5) | $ -2 $ |
| (-5, -3), (5, -5) | $ -\frac{1}{5} $ |
| (2, -5), (0, 5) | $ -5 $ |
| (-5, 0), (5, -2) | $ -\frac{1}{5} $ |
| (-5, -4), (5, -1) | $ \frac{3}{10} $ |
Let me know if you'd like these explained in a different way or visualized!
Parent Tip: Review the logic above to help your child master the concept of algebra slope worksheet.
