Slope and Proportional Relationships Worksheet with Answers – Grade 8 (Free PDF)

Problem 1 Is the table proportional? ★★★

Decide whether each table is proportional. If it is, give the constant of proportionality.

Table 1

Table 2

Problem 2 Hiking rate ★★★

A hiker walks 7.5 miles in 3 hours at a steady pace. Find the unit rate and write an equation for the distance y after x hours.

Problem 3 Slope from two points ★★★

Find the slope of the line through: (a) (1, 3) and (4, 12) (b) (2, −1) and (6, 7)

Problem 4 Equation from a graph ★★★

The graph shows a proportional relationship. Write its equation.

Problem 5 Printer speed ★★★

A printer prints 24 pages in 4 minutes. Write an equation relating pages y to minutes x.

Problem 6 Read the slope ★★★

Use the labeled slope triangle to find the slope of the line.

Problem 7 Which machine is faster? ★★★

Machine A fills y = 4.5x gallons in x minutes. Machine B fills 10 gallons in 2 minutes, 20 in 4 minutes and 30 in 6 minutes. Which machine fills faster, and by how much per minute?

Problem 8 Graph versus equation ★★★

Graph: a line through the origin and (4, 10). Equation: y = 2.8x. Which relationship has the greater unit rate?

Problem 9 Similar slope triangles ★★★

Two slope triangles are drawn on a line. The small one has run 3 and rise 2. The large one has run 9 and rise 6. Show that they give the same slope and explain why using similar triangles.

Problem 10 Finding missing coordinates ★★★

A line through the origin has slope 34. Find y when x = 8, and find x when y = 15.

Problem 11 Slope and intercept ★★★

Name the slope and the y-intercept: (a) y = −6x + 5 (b) y = 25x − 8 (c) y = 9x

Problem 12 Write the equation from a graph ★★★

Find the slope and y-intercept of the line, then write its equation in the form y = mx + b.

Problem 13 Negative slopes ★★★

Find the slope of the line through: (a) (−2, 5) and (4, −1) (b) (3, 8) and (7, 2)

Problem 14 Zero and undefined slope ★★★

Find the slope of the horizontal line y = 4 and of the vertical line x = 3. Explain each answer.

Problem 15 Smoothie mango ★★★

A smoothie shop uses 1.5 cups of mango for every 4 smoothies. Write an equation for the cups y needed for x smoothies. Then find the cups for 30 smoothies.

Problem 16 Dog walkers ★★★

Dana earns y = 13.5x dollars for x hours. Eli earns $42 for 3 hours and $70 for 5 hours at a steady rate. Who earns more per hour? How much more would that person earn in an 8-hour day?

Problem 17 Charity walk ★★★

Leo’s walk is shown by the graph through the origin and (4, 8.5), with hours on the x-axis and miles on the y-axis. Zoe walks y = 2.25x. Who is faster, and how many more miles does that walker cover in 6 hours?

Problem 18 Collinear points ★★★

Points A(1, 2), B(3, 5) and C(5, 8) are plotted. Decide whether they lie on one line by comparing slopes, and explain with similar triangles.

Problem 19 Taxi fare ★★★

A taxi charges $3.50 plus $2.25 per mile. Write an equation for the fare y after x miles, find the fare for an 8-mile ride, and say whether the relationship is proportional.

Problem 20 Line through two points ★★★

A line passes through (2, 5) and (6, 13). Find its slope, its equation, and its y value when x = 10.