Question 641·Hard·Math

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A recreation center loads each member’s activity card with credits at the start of every month. Every time a member reserves a spot in a yoga class, $12$ credits are deducted from the card. The relationship between the number of yoga classes reserved, $x$ , and the number of credits remaining on the card, $y$ , is modeled by the equation

y + 12x = 150

What is the best interpretation of $150$ in this context?

A linear model with a fixed deduction per action has a starting amount and an amount spent for each action. Set the action count to $0$ to find the starting amount. Graph the equation in Desmos and click its vertical-axis crossing to check. Keep the units straight: credits are not a count of classes.

Hints

Hint 1
The input $x$ counts reservations. At zero reservations, no credits have been deducted. What value of $x$ represents the balance loaded at the start of the month?
Hint 2
The y-intercept is where a graph crosses the vertical axis, so $x=0$ there. Read the point’s $y$ -coordinate in credits, not in classes.

Step-by-step

Find the starting balance
Step 1
Represent the start of the month
Because $x$ counts classes reserved, before any class means $x=0$ . The y-intercept is the balance when the input is zero, so put $0$ in for $x$ :
$y+12(0)=150.$
Step 2
Read the balance at zero classes
Type $y+12x=150$ in Desmos and click where the line crosses the vertical axis. Desmos shows $(0,150)$ . At $x=0$ classes, $y=150$ credits remain, so the card initially contains $150$ credits before any yoga classes are reserved. Choice B.

Question 641·Hard·Math

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