Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 7th grade proportional equations? Then this Grade 7 lesson on Writing and Using y = kx Equations explains each idea step by step, with worked examples.
Quick answer: An equation of a proportional relationship has the form y = kx, where k is the constant of proportionality, the unit rate. To write it, divide any y-value by its x-value to find k. Then use the equation to find missing values or to compare rates across tables, graphs and stories.
Standards: 7.RP.A.2c · Level: Grade 7
What is the equation of a proportional relationship?
Every proportional relationship can be written as one short equation. If y is the amount that depends on x, then y equals the constant of proportionality times x.
y = kx
Here k is the unit rate. In a store, with total cost t, price per item p and number of items n, the same idea reads t = pn.
How do you write the equation from a table, graph or story?
- Find k: divide any y by its x, or read the y-value at x = 1 on a graph, or take the rate from the story.
- Check a second pair, so you know the relationship really is proportional.
- Write y = kx with the number in place of k.
- To find y, multiply k by x. To find x, divide y by k.
The line in the graph passes through (4, 18). Then k = 18 ÷ 4 = 4.5, so the equation is y = 4.5x. At x = 10, y = 4.5 × 10 = 45. For y = 63, x = 63 ÷ 4.5 = 14. Answer: y = 4.5x.
How do you compare two proportional relationships?
Find the constant of proportionality of each one, whatever its form: a table, a graph, an equation or a sentence. The larger k means the faster rate and, on a graph, the steeper line through the origin.
Writing y = x ÷ k or x = ky by accident. The constant always multiplies the input: check by substituting a known pair.
Say the equation as a sentence: "the output is 4.5 times the input." If the sentence matches the story, the equation is right.
- The equation y = kx models every proportional relationship.
- Find k by dividing y by x for any pair in the table, or read it at x = 1 on the graph.
- To find a missing y, multiply by k; to find a missing x, divide by k.
- In a store, total cost t = pn, with price p per item and n items.
- Compare relationships by comparing their constants of proportionality.
Writing and Using y = kx Equations: frequently asked questions
How do you write y = kx from a table?
Divide one y-value by its matching x-value to get k, check one more pair, and then write y = kx with that number. For example, 18 and 4 give k = 4.5, so y = 4.5x.
What does k represent?
It is the amount of y for each 1 unit of x, the unit rate. In t = pn, k is the price per item p.
How do I find x when I know y?
Divide y by k. If y = 4.5x and y = 63, then x = 63 divided by 4.5, which is 14.
How can I compare relationships in different forms?
Convert each one to its constant of proportionality. Read it from the equation, compute y divided by x in the table, or read the point at x = 1 on the graph, then compare the numbers.
Can the equation have a fraction for k?
Yes. If 3 feet are covered in 8 minutes, then distance d = (3/8)t. You can also use a decimal such as 0.375 when that is easier.