Question 621·Easy·Math

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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?

On a graph, slope measures the change in $y$ for each unit of change in $x$ . Read two points you can locate exactly, then put the change in $y$ over the change in $x$ . Subtract in the same order for both changes: a line that falls as you move right must have a negative slope.

Hints

Hint 1
A point’s coordinates give its horizontal position first and vertical position second. Read the two solid dots on the graph. As you move from the left dot to the right dot, does $y$ rise or fall?
Hint 2
The slope is the change in $y$ divided by the change in $x$ , not either change alone. Subtract the points in the same order on top and bottom. What fraction does that give you?

Step-by-step

Read two points and find the slope
Step 1
Read the marked points
Read the two marked points directly from the graph. Their coordinates are $(-2,5)$ and $(4,-1)$ . Moving between the solid dots from left to right, $x$ increases while $y$ decreases, so expect a negative slope.
Step 2
Compare the vertical and horizontal changes
The slope is the change in $y$ divided by the change in $x$ . Subtract in the same order, going from $(-2,5)$ to $(4,-1)$ :
$m=\frac{-1-5}{4-(-2)}$
Step 3
Find the change per unit
Type $\frac{-1-5}{4-(-2)}$ in Desmos to divide the vertical drop by the horizontal increase. Desmos shows $-1$ :
$m=-1$
So the slope of $g$ is $-1$ : its graph falls $1$ unit for each unit you move right. Choice A.

Lessons that teach this

SAT AlgebraBeginnerCoreFind slope and rate of change

Question 621·Easy·Math

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