Question 347·Easy·Algebra

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The line graphed in the $xy$ -plane above models the total number of pages read, $y$ , after $x$ minutes.

According to the graph, how many pages are read per minute?

A straight-line graph of time and an amount has a slope: the steady change in the amount for each extra unit of time. The phrase pages per minute asks for that slope, not the number of pages already read at the start. Read two exact points using the axis labels, divide the change in pages by the change in minutes, and calculate the quotient in Desmos.

Hints

Hint 1
Each marked point pairs a time with a total page count. Read the coordinates from the axis labels: minutes across, pages up. The page axis increases by $2$ at each tick, so don't count each vertical tick as one page.
Hint 2
A unit rate tells you how many pages are read in one minute. Subtract the page totals at the marked points, then subtract the times in the same order. Which change goes above the fraction bar?

Step-by-step

Find the rate from two points
Step 1
Read the marked points
The marked point $(0,4)$ means $4$ pages have been read at $0$ minutes. The other point, $(6,22)$ , means $22$ pages have been read at $6$ minutes. Use the axis labels to read them: each vertical tick represents $2$ pages.
Step 2
Write the change in pages per minute
The slope of this line is the change in pages divided by the change in minutes. Go from $(0,4)$ to $(6,22)$ and subtract in the same order on top and bottom:
$\frac{22-4}{6-0}\text{ pages per minute}.$
Put the change in pages over the change in time. The $4$ pages at the start aren't pages added during these $6$ minutes.
Step 3
Calculate and interpret the rate
Type $\frac{22-4}{6-0}$ into Desmos. It shows $3$ , so the reading rate is $3$ pages per minute. Choice B.

Question 347·Easy·Algebra

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