The graph of the linear function is shown, where . Which choice gives the slope of the line?

Solution available with step-by-step explanation

SAT Linear Functions Question 16 | Free SAT Prep | Aniko

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Question 16·Easy·Linear Functions

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The graph of the linear function $g$ is shown, where $y=g(x)$ . Which choice gives the slope of the line?

For slope-from-graph questions, choose two clear points on the line (preferably marked points), then use $\text{slope}=\dfrac{\Delta y}{\Delta x}$ . Keep track of the sign: a line that goes down from left to right has a negative slope.

Hints

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Pick two marked points

Use the two labeled points shown on the line to calculate slope.

Use rise over run

Compute $\dfrac{\text{change in }y}{\text{change in }x}$ using those two points.

Watch the sign

If the line goes down as you move to the right, the slope should be negative.

Desmos Guide

Enter the two points

Plot the points $(-2,5)$ and $(4,-1)$ as two ordered pairs.

Use a slope calculation

In a new line, type (y2-y1)/(x2-x1) and substitute the coordinates from the two plotted points: use $y2=-1$ , $y1=5$ , $x2=4$ , and $x1=-2$ .

Interpret the value

The computed value is the slope of the line; match it to the answer choices.

Step-by-step Explanation

Use two points to find rise over run

From the graph, the line passes through the points $(-2, 5)$ and $(4, -1)$ . The slope is

\text{slope} = \frac{-1-5}{4-(-2)} = \frac{-6}{6}.

Simplify

Simplify $\frac{-6}{6}$ to get $-1$ , so the slope of the line is $-1$ .

Strategy

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Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation