SAT Linear Functions Question 13 | Free SAT Prep

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Question 13·Easy·Linear Functions

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

For slope questions with two points, immediately write down the slope formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ , label your points clearly, and plug in carefully while keeping the order of subtraction consistent in the numerator and denominator. Do the subtractions one at a time, watch out for minus signs—especially when subtracting negative numbers—and then simplify the fraction, checking that the sign (positive or negative) matches whether the line goes up or down as $x$ increases.

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Use the slope formula

The slope of a line through two points is given by $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ . Identify $x_1, y_1, x_2, y_2$ from the coordinates.

Be consistent with your order

Once you choose which point is $(x_1, y_1)$ , use the other point as $(x_2, y_2)$ and keep that same order in both the numerator and denominator.

Carefully subtract the coordinates

Compute $y_2 - y_1$ and $x_2 - x_1$ step by step. Pay special attention to subtracting negative numbers in the denominator.

Simplify the fraction

After you have the fraction for the slope, reduce it to simplest form and notice its sign (positive or negative).

Desmos Guide

Enter the slope expression

In Desmos, type the expression (-5 - 7) / (2 - (-4)) exactly as it appears, using parentheses around each subtraction.

Interpret the output

Look at the numerical value Desmos displays for this expression; that value is the slope of the line through the two given points.

Step-by-step Explanation

Recall the slope formula and label the points

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is

m = \frac{y_2 - y_1}{x_2 - x_1}.

Let $(-4, 7)$ be $(x_1, y_1)$ and $(2, -5)$ be $(x_2, y_2)$ .

Find the change in y (rise)

Compute $y_2 - y_1$ using the given points:

y_2 - y_1 = -5 - 7.

Work this out carefully: subtracting 7 from $-5$ gives a negative number.

Find the change in x (run)

Compute $x_2 - x_1$ using the given points:

x_2 - x_1 = 2 - (-4).

Remember that subtracting a negative is the same as adding.

Form the fraction and simplify to get the slope

Now substitute the differences into the slope formula:

\begin{aligned} m &= \frac{y_2 - y_1}{x_2 - x_1} \\ &= \frac{-5 - 7}{2 - (-4)} \\ &= \frac{-12}{6} \\ &= -2. \end{aligned}

So, the slope of the line is $-2$ .

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation