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.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
A plumber charges a $75 call-out fee plus $50 per hour.
What is the total cost of a six-hour job?
A tank holds 500 gallons and drains at 12 gallons per minute.
How much is left after 15 minutes?
“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.
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.
Find the slope
Find the intercept
Assemble it
Use it
A check worth thirty seconds
Test your equation at \(x = 0\) and \(x = 1\) against the sentence. At zero months the gym should cost $40, and 25(0) + 40 = 40. At one month it should cost $65, and 25(1) + 40 = 65.
If you had written it the other way round, \(x = 0\) would give $25, which does not match a $40 sign-up fee. That check catches the swap every time, and the swap is the only real way to lose this question.