Explanation:
We need to find the slope of a line that passes through each given pair of points.
The slope formula is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let’s go through each pair one by one.
---
1. Points: (-1, -4) and (3, -3)
Let \((x_1, y_1) = (-1, -4)\), \((x_2, y_2) = (3, -3)\)
\[
\text{slope} = \frac{-3 - (-4)}{3 - (-1)} = \frac{-3 + 4}{3 + 1} = \frac{1}{4}
\]
✔ Slope = \( \frac{1}{4} \)
---
2. Points: (1, -5) and (-4, 5)
\((x_1, y_1) = (1, -5)\), \((x_2, y_2) = (-4, 5)\)
\[
\text{slope} = \frac{5 - (-5)}{-4 - 1} = \frac{5 + 5}{-5} = \frac{10}{-5} = -2
\]
✔ Slope = \(-2\)
---
3. Points: (-5, -3) and (5, -5)
\((x_1, y_1) = (-5, -3)\), \((x_2, y_2) = (5, -5)\)
\[
\text{slope} = \frac{-5 - (-3)}{5 - (-5)} = \frac{-5 + 3}{5 + 5} = \frac{-2}{10} = -\frac{1}{5}
\]
✔ Slope = \( -\frac{1}{5} \)
---
4. Points: (2, -5) and (0, 5)
\((x_1, y_1) = (2, -5)\), \((x_2, y_2) = (0, 5)\)
\[
\text{slope} = \frac{5 - (-5)}{0 - 2} = \frac{5 + 5}{-2} = \frac{10}{-2} = -5
\]
✔ Slope = \(-5\)
---
5. Points: (-5, 0) and (5, -2)
\((x_1, y_1) = (-5, 0)\), \((x_2, y_2) = (5, -2)\)
\[
\text{slope} = \frac{-2 - 0}{5 - (-5)} = \frac{-2}{10} = -\frac{1}{5}
\]
✔ Slope = \( -\frac{1}{5} \)
---
6. Points: (-5, -4) and (5, -1)
\((x_1, y_1) = (-5, -4)\), \((x_2, y_2) = (5, -1)\)
\[
\text{slope} = \frac{-1 - (-4)}{5 - (-5)} = \frac{-1 + 4}{5 + 5} = \frac{3}{10}
\]
✔ Slope = \( \frac{3}{10} \)
Let me double-check all calculations quickly:
1. (−1,−4) → (3,−3): Δy = 1, Δx = 4 → 1/4 ✔
2. (1,−5) → (−4,5): Δy = 10, Δx = −5 → −2 ✔
3. (−5,−3) → (5,−5): Δy = −2, Δx = 10 → −1/5 ✔
4. (2,−5) → (0,5): Δy = 10, Δx = −2 → −5 ✔
5. (−5,0) → (5,−2): Δy = −2, Δx = 10 → −1/5 ✔
6. (−5,−4) → (5,−1): Δy = 3, Δx = 10 → 3/10 ✔
All correct.
Final Answer:
1/4, −2, −1/5, −5, −1/5, 3/10
Parent Tip: Review the logic above to help your child master the concept of slope math worksheet.
