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All courses Algebra II · A-CED.2 16 of 55
Create equations in two or more variables, graph them, and interpret relationships with labels and scales.

Write an equation in two variables from a context

Problem
A rectangle has width \(x\), length \(y\), and area \(60\). Write an equation relating \(x\) and \(y\).
Your answer
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Hint

Identify which formula connects width, length, and area for a rectangle.

For a rectangle, area is found by multiplying width by length.

Solution walkthrough

01

Name the rectangle dimensions

\[\text{width}=x;~\text{length}=y\]

The prompt assigns x to the width and y to the length.

02

Use the area relationship

\[\text{area}=\text{width}*\text{length}\]

A rectangle's area is the product of its two perpendicular side lengths.

03

Substitute the given area

\[60=x*y\]

The rectangle's area is 60, so the dimension product must equal 60.

04

State the equation

\[xy~=~60\]

Reordering the equality gives the requested two-variable relationship xy=60, choice A.

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Another way

  1. Solve for either variable to get y=60/x or x=60/y, equivalent forms when the corresponding dimension is nonzero.

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Common mistake

Do not add the dimensions or write 2x+2y=60; that expression represents perimeter, while the prompt gives area.

Solution walkthrough video