Question

a line that includes the points (-10, 7) and (4, q) has a slope of -\frac{8}{7}. what is the value of q?

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, $x_1=-10,y_1 = 7,x_2 = 4,y_2=q$ and $m=-\frac{8}{7}$.
$$-\frac{8}{7}=\frac{q - 7}{4-(-10)}$$

Step2: Simplify the denominator

Simplify the denominator of the right - hand side. $4-(-10)=4 + 10=14$. So the equation becomes $-\frac{8}{7}=\frac{q - 7}{14}$.

Step3: Cross - multiply

Cross - multiply to get $-8\times14=7\times(q - 7)$.
$$-112 = 7q-49$$

Step4: Solve for $q$

Add 49 to both sides of the equation: $-112 + 49=7q$, so $-63 = 7q$. Then divide both sides by 7: $q=-9$.

Answer:

$-9$