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All courses Math I · A-SSE.1.a 13 of 59
Interpret terms, factors, and coefficients in linear and exponential expressions.

Interpret a coefficient as a rate or per-unit change

Problem
In C=8t+20, C is dollars and t is tickets. Enter coefficient, signed output change, and per-input-unit rate.
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Hint

Look at the number multiplying t in 8t.

In a linear expression, the coefficient tells how much the output changes for each increase of 1 in the variable.

Solution walkthrough

01

Identify the coefficient

\[C~=~8t~+~20\]

The coefficient of t is 8 because 8 is the number multiplying t.

02

Connect it to the variable

\[t~=~\text{number of tickets}\]

Each time the number of tickets increases by 1, the term 8t increases by 8.

03

Interpret the coefficient

\[\text{coefficient}~=~8;~\text{output}~\text{change}~=~+\$8;~\text{per}~\text{input}~\text{unit}~=~1~\text{ticket};~\text{rate}~=~+\$8/\text{ticket}\]

So the coefficient 8 means each additional ticket adds 8 dollars to the total cost.

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Another way

  1. Compare two nearby values: from 1 ticket to 2 tickets, the total increases by 8 dollars.

  2. Read 8t as 8 dollars per ticket times the number of tickets.

!

Common mistake

Calling 8 the starting fee instead of noticing it changes with the number of tickets.