Question

analyzing a students work
anya found the slope of the line that passes through the points (-7, 4) and (2, -3). her work is shown below.
let (x2, y2) be (-7, 4) and (x1, y1) be (2, -3)
m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4-(-3)}{-7 - 2}=-\frac{7}{9}
the slope is (-\frac{7}{9}).
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 (x1, y1).
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 $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Analyze student's work

Anya labeled $(x_2,y_2)$ as $(-7,4)$ and $(x_1,y_1)$ as $(2,-3)$. The correct way is to use the change - in $y$ values over the change - in $x$ values. But she made an error in labeling the points. The point with the larger $x$ - coordinate should typically be $(x_2,y_2)$ or it doesn't matter as long as the order is consistent in the formula. Here, she has a mix - up in the order of substitution. The correct formula application would be $m=\frac{y_2 - y_1}{x_2 - x_1}$, and she labeled the points incorrectly.

Answer:

She labeled the points incorrectly. The point $(-7,4)$ should be $(x_1,y_1)$