Linear Functions Test – Grade 8 Math (Printable PDF)

Question 1 Table to rule (3 points)

The table shows a linear function.

1. Find the rate of change. (1 point)
2. Find the initial value. (1 point)
3. Write the rule. (1 point)

Question 2 Two points (3 points)

A line passes through (3, −4) and (7, 8).

1. Find the slope. (1 point)
2. Find the y-intercept. (1 point)
3. Write the equation. (1 point)

Question 3 Draining a pool (3 points)

The graph shows the gallons in a kiddie pool as it drains, with minutes on the x-axis.

1. Find the rate of change and the initial value. (1 point)
2. Write the function. (1 point)
3. When is the pool empty? (1 point)

Question 4 Trail club fees (3 points)

A trail club charges a $25 membership fee plus $9 per guided hike.

1. Write a function for the total cost y of x hikes. (1 point)
2. Find the cost of 8 hikes. (1 point)
3. Explain what 9 and 25 mean. (1 point)

Question 5 Hiker’s elevation (3 points)

The graph shows a hiker’s elevation over time. Describe each section. (1 point each)

1. Section A
2. Section B
3. Section C

Question 6 Sketch a story (2 points)

A kayaker paddles at a steady speed, rests for a while, then paddles at a faster steady speed. Sketch a graph of distance paddled against time. (2 points)

Question 7 Drone model (2 points)

A drone is 12 feet high after 1 second and 36 feet high after 4 seconds, climbing steadily. Find the rate of change (1 point) and write the function (1 point).

Question 8 Linear or not? (1 point)

A table shows x = 1, 2, 3 and y = 1, 4, 9. Is the function linear? Justify. (1 point)