Question

anya found the slope of the line that passes through the points (-7, 4) and (2, -3). her work is shown below. let ((x_2, y_2)) be ((-7, 4)) and ((x_1, y_1)) be ((2, -3)). (m = \frac{x_2 - x_1}{y_2 - y_1}) (= \frac{-7 - 2}{4 - (-3)}) (= -\frac{9}{7}) the slope is (-\frac{9}{7}). what error did she make?

• she simplified the denominator incorrectly. the denominator simplifies to -7.
• she labeled the points incorrectly. the point ((-7, 4)) should be ((x_1, y_1)).
• she used an incorrect formula. the formula should be the change in (y)-values with respect to the change in the (x)-values.
• she used an incorrect formula. the formula should be the sum of the (x)-values with respect to the sum of the (y)-values.

Explanation:

Step1: Recall slope formula

The slope formula for points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Analyze Anya's work

Anya wrote $m=\frac{x_2-x_1}{y_2-y_1}$, swapping x and y values.

Step3: Match to error options

Her error is using the wrong formula: slope is change in y over change in x.

Answer:

She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values.