The line graphed in the -plane above models the total number of pages read, , after minutes. According to the graph, how many pages are read per minute?

Solution available with step-by-step explanation

SAT Linear Functions Question 70 | Free SAT Prep | Aniko

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Question 70·Easy·Linear Functions

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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?

For a linear-function graph, the constant rate is the slope. Pick any two visible points on the line and compute slope as $\frac{\text{change in }y}{\text{change in }x}$ . Here, that slope represents pages per minute.

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Use the rate of change

Pages read per minute is the line’s slope (rise over run).

Pick two clear points

Use two points that are marked on the graph, such as $(0,4)$ and $(6,22)$ .

Compute rise over run

Find the change in pages and divide by the change in minutes.

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Plot the marked points

In a table, enter the points $(0,4)$ and $(6,22)$ .

Create a line with an adjustable slope

Type $y=mx+4$ so that $m$ becomes a slider (the $4$ matches the point at $x=0$ ).

Match the graph to the second point

Adjust $m$ until the line passes through the point $(6,22)$ . The value of $m$ is the pages-per-minute rate.

Step-by-step Explanation

Use two points to set up the slope

From the graph, the line passes through $(0,4)$ and $(6,22)$ . The slope is

\frac{22-4}{6-0}=\frac{18}{6}

This slope represents pages per minute.

Simplify and state the answer

Simplify $\frac{18}{6}$ to get $3$ . Therefore, the number of pages read per minute is $3$ .

Strategy

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Step-by-step Explanation

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Strategy

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Step-by-step Explanation