Question 617·Easy·Algebra

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The graph of the linear function $f$ is shown above, where $y=f(x)$ .

Which choice is the slope of the graph of $f$ ?

A line’s slope is its vertical change divided by its horizontal change. On a graph with marked points, read their coordinates, then put the change in $y$ over the change in $x$ ; Desmos can evaluate the fraction. Subtract in the same order on top and bottom. A line rising to the right should have a positive slope.

Hints

Hint 1
A slope measures how much a line rises for each unit it moves right. Use the two marked points to find those changes exactly, rather than estimating from the drawing.
Hint 2
The rise is the change in $y$ , and the run is the change in $x$ . Put rise over run, subtracting the coordinates in the same order. Should your slope be positive or negative?

Step-by-step

Find rise over run from the marked points
Step 1
Read the points and check the direction
Read the two solid points against the axes: $(2,1)$ and $(8,5)$ . Moving from the first point to the second, both $x$ and $y$ increase, so the slope (the line’s rate of change) must be positive.
Step 2
Put the vertical change over the horizontal change
Slope is the change in $y$ , called the rise, divided by the change in $x$ , called the run. Use second minus first in both places:
$m=\frac{\text{change in }y}{\text{change in }x}$ $m=\frac{5-1}{8-2}$
Reversing only one subtraction would give a negative slope, which wouldn't fit the rising line.
Step 3
Evaluate the slope
Type $\frac{5-1}{8-2}$ into Desmos. It shows approximately $0.667$ ; click the fraction button to see $\frac{2}{3}$ . The result is positive, as the graph predicts, so the slope of $f$ is $\frac{2}{3}$ . Choice A.

Lessons that teach this

SAT AlgebraBeginnerCoreFind slope and rate of change

Question 617·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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