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MAT-144 · In-person sections Exam 1 Review · Unit 1
Exam 1 Review · Q19

Building a linear equation from a description, then using it

Two numbers are hidden in the sentence: one that repeats and one that happens once. Find which is which and the equation writes itself.

Every step of Building a linear equation from a description, then using it explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

A service call

A plumber charges a $75 call-out fee plus $50 per hour.

What is the total cost of a six-hour job?

$
A negative slope

A tank holds 500 gallons and drains at 12 gallons per minute.

How much is left after 15 minutes?

Just the slope

“A used car is worth $14,000 today and loses $1,200 of its value each year.”

What is the slope of the linear model? Include the sign.

m =
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
the per amount is the slope \(m\) per month, per hour, per mile, each time
the one-off amount is the intercept \(b\) the value before anything happens
Then \(y = mx + b\), and evaluating is substitution. The whole question turns on sorting the two numbers correctly, which is why swapping them is the error worth guarding against.
Common slips
(1) Swapped \(m\) and \(b\). The number attached to a “per” multiplies the variable; the standalone number does not. (2) Missed a negative slope. Drains, falls, loses and decreases all mean \(m\) is negative. (3) Answered with the equation when the question wanted a value, or the other way round. These questions usually ask for both, in two parts.
Sort the two numbers

A gym charges a $40 sign-up fee plus $25 per month.

Write the total cost \(C\) after \(m\) months, then find the cost of a nine-month membership.

Step 1

Find the slope

Which number repeats every month? That is \(m\).
$
Step 2

Find the intercept

Which number is charged once, before any months pass? That is \(b\).
$
Step 3

Assemble it

Which equation is right?
Step 4

Use it

What does nine months cost? Substitute \(m = 9\).
$