← Back to the Slope And Proportional Relationships worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.EE.B.5, 8.EE.B.6 · Level: Grade 8
Problem 1 Is the table proportional?
Table 1: 7 ÷ 2 = 3.5, 14 ÷ 4 = 3.5, 21 ÷ 6 = 3.5: constant. Table 2: 5 ÷ 1 = 5 but 9 ÷ 2 = 4.5: not constant.
Table 1 is proportional with k = 3.5; Table 2 is not.
Problem 2 Hiking rate
7.5 ÷ 3 = 2.5 miles per hour. The distance is the rate times the time.
y = 2.5x
Problem 3 Slope from two points
(a) Rise = 12 − 3 = 9 and run = 4 − 1 = 3, so 9 ÷ 3 = 3. (b) Rise = 7 − (−1) = 8 and run = 6 − 2 = 4, so 8 ÷ 4 = 2.
(a) 3 (b) 2
Problem 4 Equation from a graph
The line passes through (4, 6). The unit rate is 6 ÷ 4 = 1.5.
y = 1.5x
Problem 5 Printer speed
24 ÷ 4 = 6 pages per minute, so the equation is y = 6x.
y = 6x
Problem 6 Read the slope
Slope = rise ÷ run = 2 ÷ 5 = 0.4. Both the rise and the run are measured left to right.
Slope = 25 = 0.4
Problem 7 Which machine is faster?
B: 10 ÷ 2 = 5 gallons per minute, the same for each pair. A: 4.5 gallons per minute. The difference is 5 − 4.5 = 0.5.
Machine B, by 0.5 gallon per minute
Problem 8 Graph versus equation
Graph: 10 ÷ 4 = 2.5. Equation: 2.8. Since 2.8 > 2.5, the equation is steeper.
The equation y = 2.8x has the greater unit rate.
Problem 9 Similar slope triangles
Small: 2 ÷ 3. Large: 6 ÷ 9 = 2 ÷ 3. The triangles share the angle at the origin and each has a right angle, so they are similar, and corresponding sides are in the same ratio.
Both slopes equal 23.
Problem 10 Finding missing coordinates
The equation is y = 34x. When x = 8: y = 34 · 8 = 6. When y = 15: 15 = 34x, so x = 15 · 43 = 20.
y = 6; x = 20
Problem 11 Slope and intercept
Compare each with y = mx + b. (a) m = −6, b = 5. (b) m = 25, b = −8. (c) m = 9, b = 0.
(a) −6 and 5 (b) 25 and −8 (c) 9 and 0
Problem 12 Write the equation from a graph
The line crosses the y-axis at (0, 5), so b = 5. From (0, 5) to (4, 7): rise 2, run 4, slope 12.
y = 12x + 5
Problem 13 Negative slopes
(a) Rise = −1 − 5 = −6 and run = 4 − (−2) = 6, so slope −1. (b) Rise = 2 − 8 = −6 and run = 7 − 3 = 4, so −6 ÷ 4 = −32.
(a) −1 (b) −32
Problem 14 Zero and undefined slope
On y = 4 the rise between any two points is 0, so 0 ÷ run = 0. On x = 3 the run is 0, and dividing by 0 is undefined.
Horizontal: slope 0. Vertical: slope undefined.
Problem 15 Smoothie mango
Unit rate: 1.5 ÷ 4 = 0.375 cup per smoothie, so y = 0.375x. For 30 smoothies: 0.375 · 30 = 11.25.
y = 0.375x; 11.25 cups
Problem 16 Dog walkers
Eli: 42 ÷ 3 = 14 and 70 ÷ 5 = 14, so $14 per hour. Dana: $13.50. Difference: $0.50 per hour, so 0.50 · 8 = $4.00 in 8 hours.
Eli, by $4.00 in 8 hours
Problem 17 Charity walk
Leo: the slope is 8.5 ÷ 4 = 2.125 miles per hour. Zoe: 2.25 miles per hour. In 6 hours Zoe walks 2.25 · 6 = 13.5 miles and Leo walks 2.125 · 6 = 12.75 miles.
Zoe is faster, by 0.75 mile in 6 hours
Problem 18 Collinear points
Slope AB = (5 − 2) ÷ (3 − 1) = 32. Slope BC = (8 − 5) ÷ (5 − 3) = 32. The slope triangles on AB and BC are congruent, so the segments have the same steepness and meet at B: the three points are collinear.
Yes, all three points lie on one line (slope 32).
Problem 19 Taxi fare
Fare: y = 2.25x + 3.5. For 8 miles: 2.25 · 8 + 3.5 = 18 + 3.5 = 21.5. At 0 miles the fare is $3.50, not $0, so the graph misses the origin.
y = 2.25x + 3.5; $21.50; not proportional
Problem 20 Line through two points
Slope = (13 − 5) ÷ (6 − 2) = 2. Use y = 2x + b with (2, 5): 5 = 4 + b, so b = 1. At x = 10: 2 · 10 + 1 = 21.
Slope 2; y = 2x + 1; y = 21