Of course! Let's solve each problem step by step. The slope of a line is calculated using the formula:
Slope (m) = Rise / Run = (Change in y) / (Change in x) = (y₂ - y₁) / (x₂ - x₁)
We will identify two points on each line from the graph, calculate the rise (vertical change) and run (horizontal change), and then find the slope.
---
Problem 1
Points: (-3, 2) and (-1, -2)
-
Rise (Δy): -2 - 2 =
-4
-
Run (Δx): -1 - (-3) = -1 + 3 =
+2
-
Slope = Rise / Run = -4 / 2 = -2
✔ Slope = -2
---
Problem 2
Points: (-3, 1) and (1, 4)
-
Rise (Δy): 4 - 1 =
+3
-
Run (Δx): 1 - (-3) = 1 + 3 =
+4
-
Slope = Rise / Run = 3 / 4
✔ Slope = 3/4
---
Problem 3
Points: (-4, 2) and (4, 0)
-
Rise (Δy): 0 - 2 =
-2
-
Run (Δx): 4 - (-4) = 4 + 4 =
+8
-
Slope = Rise / Run = -2 / 8 = -1/4
✔ Slope = -1/4
---
Problem 4
Points: (-4, -4) and (1, 1)
-
Rise (Δy): 1 - (-4) = 1 + 4 =
+5
-
Run (Δx): 1 - (-4) = 1 + 4 =
+5
-
Slope = Rise / Run = 5 / 5 = 1
✔ Slope = 1
---
Problem 5
Points: (-4, -3) and (1, -3)
-
Rise (Δy): -3 - (-3) =
0
-
Run (Δx): 1 - (-4) = 1 + 4 =
+5
-
Slope = Rise / Run = 0 / 5 = 0
This is a
horizontal line, so the slope is always
0.
✔ Slope = 0
---
Problem 6
Points: (-4, -3) and (-2, 3)
-
Rise (Δy): 3 - (-3) = 3 + 3 =
+6
-
Run (Δx): -2 - (-4) = -2 + 4 =
+2
-
Slope = Rise / Run = 6 / 2 = 3
✔ Slope = 3
---
##
✔ Final Answers:
1)
Slope = -2
2)
Slope = 3/4
3)
Slope = -1/4
4)
Slope = 1
5)
Slope = 0
6)
Slope = 3
Let me know if you'd like to see these plotted or explained visually!
Parent Tip: Review the logic above to help your child master the concept of calculating slope worksheet.
