Question 609·Easy·Math

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A line passes through the points $(-4,7)$ and $(2,-5)$ . What is the slope of the line?

Two points on a line are enough to find its slope, the change in $y$ for each $1$ -unit increase in $x$ . Put the change in $y$ over the change in $x$ , then type the fraction into Desmos. Subtract the points in the same order on top and bottom; switching the order on only one side flips the sign.

Hints

Hint 1
The slope compares how much $y$ changes with how much $x$ changes. Put the change in $y$ on top. Which coordinates will you subtract on the bottom?
Hint 2
Move from $(-4,7)$ to $(2,-5)$ . Subtract the first $y$ from the second $y$ , and the first $x$ from the second $x$ . Using the same order keeps the sign correct.

Step-by-step

Find the slope from the two points
Step 1
Check whether the line rises or falls
From $(-4,7)$ to $(2,-5)$ , $x$ increases while $y$ decreases. The line falls as you move right, so its slope must be negative.
Step 2
Set up the slope
Slope is the change in $y$ divided by the change in $x$ . Subtract the first point from the second in both places:
$m=\frac{-5-7}{2-(-4)}.$
Step 3
Evaluate and interpret the result
Type $\frac{-5-7}{2-(-4)}$ into Desmos. It prints $-2$ : $y$ falls by $12$ while $x$ increases by $6$ , so the line's slope is $-2$ . Choice A.

Lessons that teach this

SAT AlgebraBeginnerCoreFind slope and rate of change

Question 609·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

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