Writing Equations for Proportional Relationships (A)

Sep 23, 2026

Worksheet for learning proportional relationships by writing linear equations in the form y = kx. Students find the constant of proportionality k from tables by dividing y by x, then form equations and use them to compute missing values in multi-step practice items. It also includes problems that require translating descriptions and word statements into equations, solving for hours, pages, gallons, costs, minutes, and additional challenge work using constant rates.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Part 1—Find k from the Table, Write the Equation

Part 2—Write the Equation from the Description

Part 3—Use the Equation to Find the Missing Value

Part 4—Word Problems

Answer Key

Name: ______________________________________ Writing Equations for Proportional Relationships (A) Remember: If y is proportional to x, the relationship can be written as y = kx, where k is the constant of proportionality. Find k by dividing any y-value by its x-value: k = y ÷ x. Then substitute known values to solve for unknowns. Directions: Find k, write the equation y = kx, and use it to solve problems. Part 1—Find k from the Table, Write the Equation 1.) hours worked / $ earned | x | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | | y | 5 | 10 | 15 | 20 | k = y ÷ x = Equation: y = x 2.) gallons / miles driven | x | 2 | 4 | 6 | 8 | | --- | --- | --- | --- | --- | | y | 3 | 6 | 9 | 12 | k = y ÷ x = Equation: y = x 3.) cups flour / cups sugar | x | 3 | 6 | 9 | 12 | | --- | --- | --- | --- | --- | | y | 1 | 2 | 3 | 4 | k = y ÷ x = Equation: y = x 4.) inches / centimeters | x | 4 | 8 | 12 | 16 | | --- | --- | --- | --- | --- | | y | 3 | 6 | 9 | 12 | k = y ÷ x = Equation: y = x Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) Part 2—Write the Equation from the Description 5.) A car travels 60 miles per hour. Equation: 6.) Apples cost $1.25 per pound. Equation: Part 3—Use the Equation to Find the Missing Value 9.) Equation: y = 4x hours / pages read If x = 7, find y. y = 10.) Equation: y = 32x gallons / cost ($) If x = 8, find y. y = 7.) A recipe uses 3 cups of oats per batch. Equation: 8.) A faucet drips 2/5 of a gallon every hour. Equation: 11.) Equation: y = 5x $ earned / hours worked If y = 35, find x. x = 12.) Equation: y = 23x minutes / miles If x = 15, find y. y = Part 4—Word Problems 13.) A worker earns $12 per hour. Write an equation. How much for 9 hours? Equation: Answer: 14.) A car uses 1/4 gallon per mile. Write an equation. How much gas for 60 miles? Equation: Answer: 15.) A recipe uses 2/3 cup of sugar per dozen cookies. How much sugar for 5 dozen? Equation: Answer: 16.) Challenge Problem Lorenzo earns money working at a cafe at a constant rate. He earned $42 for 6 hours. a) Find k (his hourly rate) . Write the equation y = kx: b) How many hours does he need to work to earn $91? Show your work. Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) ANSWER KEY Part 1—Tables: 1.) k = 5 2.) k = 32 y = 5x 3 y = x 2 Part 2—Descriptions: 5.) d = 60t (k = 60) 6.) c = 5/4 p (k = 54) Part 3—Find the Missing Value: 9.) y = 28 10.) y = 12 Part 4—Word Problems: 13.) y = 12x y = 12(9) = $108 14.) y = 1/4 x y = 1/4(60) = 15 gallons 15.) y = 2/3 x y = 2/3(5) = 10/3 = 3⅓ cups 16.) Challenge: a) k = 42 ÷ 6 = $7/hr. Equation: y = 7x b) 91 = 7x → x = 91 ÷ 7 = 13 hours 1 1 3.) k = y = x 3 3 4.) k = 34 y = 34x 7.) y = 3x (k = 3) 8.) y = 2/5 x (k = 25) 11.) x = 7 12.) y = 10 Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)

FAQs

How do you find the constant of proportionality k in y = kx?

When y is proportional to x, divide any y-value by its corresponding x-value: k = y ÷ x. Then use k to write the equation y = kx.

What steps should you follow to solve for a missing value using y = kx?

Write the equation y = kx using the given k (from a table or description). Substitute the known x or y value, then solve for the unknown variable.

What do the word problems ask you to do?

Translate real situations with constant rates into an equation y = kx, then answer questions such as cost for a number of hours, gallons for a distance, or sugar for a given number of cookies.

Sep 23, 2026

Uploaded by Jordan Avery

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