Question

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{x₂ - x₁}{y₂ - y₁} = \frac{-7 - 2}{4 - (-3)} = -\frac{9}{7} the slope is -\frac{9}{7}. what error did she make? \bigcirc she simplified the denominator incorrectly. the denominator simplifies to -7. \bigcirc she labeled the points incorrectly. the point (-7, 4) should be (x₁, y₁). \bigcirc she used an incorrect formula. the formula should be the change in y - values with respect to the change in the x - values. \bigcirc 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:

The correct slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$, which uses change in $y$-values over change in $x$-values. Anya incorrectly used $m=\frac{x_2-x_1}{y_2-y_1}$, swapping the numerator and denominator of the proper slope formula.

Answer:

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