Question

a line has a slope of - 8/3 and includes the points (-10, 2) and (v, 10). what is the value of v?

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $m$ is the slope and $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Given $m = \frac{8}{3}$, $(x_1,y_1)=(-10,2)$ and $(x_2,y_2)=(v,10)$.

Step2: Substitute values into slope - formula

Substitute the values into the formula: $\frac{8}{3}=\frac{10 - 2}{v-(-10)}$.

Step3: Simplify the right - hand side

Simplify the numerator of the right - hand side: $\frac{8}{3}=\frac{8}{v + 10}$.

Step4: Cross - multiply

Cross - multiply to get $8(v + 10)=8\times3$.

Step5: Expand and solve for $v$

Expand the left - hand side: $8v+80 = 24$. Then subtract 80 from both sides: $8v=24 - 80=-56$. Divide both sides by 8: $v=-7$.

Answer:

$-7$