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All courses Math II · A-CED.2 3 of 73
Create equations in two or more variables and graph them with appropriate labels and scales.

Write a two-variable linear equation from a fixed amount and a rate

Problem
For this situation, write a two-variable linear equation: cost C is 12 dollars plus 4 dollars per item x
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Hint

Identify the fixed amount and the amount per item. The cost starts with \(12\) dollars and increases by \(4\) dollars for each item \(x\).

A linear cost model has the form \(total = rate * quantity + fixed fee\).

Solution walkthrough

01

Identify the variables

\[C~=~\text{total}~\text{cost},~x~=~\text{number}~\text{of}~\text{items}\]

The equation should connect the total cost to the number of items purchased.

02

Find the variable part

\[4x\]

Each item costs \(4\) dollars, so \(x\) items cost \(4x\) dollars.

03

Add the fixed amount

\[C~=~4x+12\]

The total includes the \(12\) dollar starting amount plus the item cost.

04

State the linear equation

\[\text{equation}:~C~=~4x+12\]

This two-variable linear equation matches the cost situation.

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Another way

  1. You can think in slope-intercept form: the slope is \(4\) dollars per item and the intercept is \(12\) dollars.

!

Common mistake

A common mistake is to write \(C=12x+4\), which swaps the fixed fee and the per-item rate.