Question

a line has a slope of - 5 and includes the points (-7,5) and (k,-5). what is the value of k?

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $m=-5$, $x_1=-7$, $y_1 = 5$, $x_2=k$, $y_2=-5$.

Step2: Substitute values into formula

$-5=\frac{-5 - 5}{k-(-7)}$, which simplifies to $-5=\frac{-10}{k + 7}$.

Step3: Cross - multiply

$-5(k + 7)=-10$.

Step4: Expand and solve for k

$-5k-35=-10$. Add 35 to both sides: $-5k=-10 + 35=25$. Divide both sides by - 5: $k=\frac{25}{-5}=-5$.

Answer:

$-5$