Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Move from reading equations to modeling steady change, then to comparing models and sketching stories without numbers.
Standards: 8.F.B.4, 8.F.B.5 · Level: Grade 8
Problem 1 Read the equation ★★★
Name the rate of change and initial value of each function: (a) y = 6x + 15 (b) c = 120 − 8t
Problem 2 Table to function ★★★
The table shows a linear function. Find the rate, the initial value and the rule.
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 20 | 26 | 32 | 38 |
Problem 3 Two points ★★★
Find the equation of the line through (2, 9) and (5, 21).
Problem 4 Gym fees ★★★
A climbing gym charges a $20 sign-up fee plus $14 per month. Write a function for the total cost y after x months and find the cost after 6 months.
Problem 5 Equation from a graph ★★★
Use the graph to determine the rule of this linear function in the form y = mx + b.
Problem 6 Describe the function ★★★
Describe each as increasing, decreasing or constant, and as linear or nonlinear: (a) y = −3x + 8 (b) y = 2x² for x ≥ 0 (c) y = 7
Problem 7 Negative coordinates ★★★
Find the equation of the line through (−2, 11) and (4, −7).
Problem 8 Table with gaps ★★★
The table shows a linear function. Write its rule.
| x | 1 | 3 | 5 | 7 |
|---|---|---|---|---|
| y | 9 | 19 | 29 | 39 |
Problem 9 Van rental meaning ★★★
The cost of renting a van is C = 0.45m + 28 dollars for m miles. Explain what 0.45 and 28 mean and find the cost of a 120-mile trip.
Problem 10 Draining tank ★★★
The graph shows the gallons in a tank over time in minutes. Find the rate of change and initial value, write the function and say when the tank is empty.
Problem 11 Drone climb ★★★
A drone is 30 feet high after 2 seconds and 54 feet high after 5 seconds, climbing at a steady rate. Write a function for its height and find the height after 10 seconds.
Problem 12 Cyclist’s trip ★★★
The graph shows a cyclist’s distance from home. Describe sections A, B and C in words and compare the speeds in A and C.
Problem 13 Sketch a story ★★★
A candle burns down at a constant rate until nothing is left. Sketch a graph of its height against time and describe it.
Problem 14 Missing values ★★★
A line through (1, 7) has slope 4. Find y when x = 6, and find x when y = 51.
Problem 15 Ride-share fare ★★★
A ride-share costs $11.50 for 3 miles and $19.00 for 6 miles. Assume the cost is linear. Find the rate per mile, the starting fee and the cost of 14 miles.
Problem 16 Phone battery ★★★
A phone battery is at 82% after 2 hours of video and 58% after 5 hours. Assume a steady drain. Write a function for the charge, find the charge after 10 hours and find when the battery reaches 0%.
Problem 17 Is a line a good model? ★★★
A table lists x = 1, 2, 3, 4 and y = 3, 6, 12, 24. Decide whether a linear function fits and describe the pattern.
Problem 18 A ball in the air ★★★
The graph shows the height of a ball thrown upward. Describe how the height changes over time, say whether the function is linear, and explain what happens at the highest point.
Problem 19 Savings race ★★★
Mia saves according to y = 15x + 60 dollars after x weeks. Noah has $20 at week 0, $100 at week 4 and $180 at week 8, at a steady rate. In which week do they have equal savings, and how much is it?
Problem 20 Candle burn time ★★★
A candle is 18 inches tall at the start and 13.5 inches tall after 3 hours. Write a function for its height, find how long it lasts, and explain why the function is not meaningful at 15 hours.
