Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Looking for a proportional equations test? Then this Grade 7 test on Writing and Using y = kx Equations checks the whole chapter, with points for each question. This test has 8 questions worth 20 points and fits 45 minutes. Show how you find the constant of proportionality, write each equation in full, and include units in word problems.
Standards: 7.RP.A.2c · Level: Grade 7
Question 1 Equation from a Table (2 points)
Write an equation relating y to x.
| x | 4 | 10 | 15 |
|---|---|---|---|
| y | 34 | 85 | 127.5 |
Question 2 Equation from a Graph (3 points)
Use the graph.
- Find the constant of proportionality. (1 point)
- Write an equation. (1 point)
- Find y when x = 14. (1 point)
Question 3 Smoothie Bar (2 points)
A smoothie costs $5.25. Write an equation for the total cost t of n smoothies, then find the cost of 13 smoothies.
Question 4 Leaking Tank (3 points)
A tank leaks 35 gallon every 4 hours at a constant rate.
- Write an equation for gallons g leaked in h hours. (1 point)
- How many gallons leak in 14 hours? (1 point)
- After how many hours have 3 gallons leaked? (1 point)
Question 5 Comparing Gym Plans (3 points)
Gym A charges according to y = 9.5x for x visits. Gym B charges as shown.
| Visits | 3 | 5 | 8 |
|---|---|---|---|
| Cost (dollars) | 30 | 50 | 80 |
- Find each gym’s cost per visit. (1 point)
- Which gym is cheaper per visit? (1 point)
- How much more does the other gym cost for 20 visits? (1 point)
Question 6 Proportional Equations (2 points)
Select every equation that models a proportional relationship, and state k for each one you select.
- y = 9x
- y = x + 9
- y = x ÷ 9
- y = 9 − x
Question 7 Graph Versus Equation (3 points)
Jada’s bike trip is shown in the graph. Eli’s distance follows d = 3.2t.
- Write Jada’s equation. (1 point)
- Who is faster? (1 point)
- How many miles ahead is the faster rider after 10 hours? (1 point)
Question 8 County Sales Tax (2 points)
The county sales tax is 6.5% of the price. Write an equation for the tax t on price p. Find the tax on an $84 item and the price of an item with $9.75 tax.

