A free printable worksheet that pairs with the Linear World Cup game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

Slope and y = mx + b

Grade 8 · CCSS 8.EE.B.6 · Pairs with the Linear World Cup game

Name

Date

Slope m = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). y = mx + b: m is the slope and b is the y-intercept, where the line crosses the y-axis at (0, b). A proportional line, y = mx, goes through the origin (b = 0).

Part A: Find the slope between two points

1. (0, 0) and (4, 6)

m =

2. (0, 2) and (3, 8)

m =

3. (0, 5) and (4, −3)

m =

4. (0, −1) and (6, 3)

m =

Part B: Proportional passes (the ball starts at the origin)

5. Pass to (4, 6).

y =

6. Pass to (5, −10).

y =

7. Pass to (3, 1).

y =

Part C: Write y = mx + b (the ball is at (0, b))

8. The ball is at (0, 2). The goal is at (6, −1).

y =

9. The ball is at (0, −3). The goal is at (4, 5).

y =

10. The ball is at (0, 4). A teammate is at (3, 10).

y =

11. The ball is at (0, 1). A teammate is at (5, 1).

y =

Part D: Read, graph and apply

12. Graph y = −½x + 2 (your answer to #8). Mark the y-intercept and the goal.

13. Name the slope and y-intercept. y = −3x + 7

m = b =

14. A taxi charges $3 plus $2 per mile. Write an equation for the cost y of a ride of x miles. What does an 8-mile ride cost?

y = cost $

15. Find the mistake. Jamie passed from (0, 0) to (4, 6) and wrote y = (4/6)x. What went wrong?

Correct: y =

Answer Key: Slope and y = mx + b

For the teacher

6 / 4 → m = 3/2
(8 − 2) / 3 = 6/3 → m = 2
(−3 − 5) / 4 = −8/4 → m = −2
(3 − (−1)) / 6 = 4/6 → m = 2/3
y = (3/2)x
−10 / 5 → y = −2x
y = (1/3)x
b = 2, m = (−1 − 2) / 6 = −1/2 → y = −(1/2)x + 2
b = −3, m = (5 − (−3)) / 4 = 2 → y = 2x − 3
b = 4, m = (10 − 4) / 3 = 2 → y = 2x + 4
b = 1, m = 0 / 5 = 0 → y = 1 (a flat pass)
Line through (0, 2) that falls 1 for every 2 to the right; it passes through (2, 1), (4, 0) and the goal at (6, −1).
m = −3, b = 7
y = 2x + 3; 2(8) + 3 = $19
Jamie wrote run over rise. Slope is rise over run: y = (3/2)x

In the game, a wrong slope sends the line (and the ball) visibly off target, and a wrong b starts the line away from the ball. Easy mode previews the line while students type.