Question

Find the value of r so the line that passes through the pair of points has the given slope.

$\left(-4,8\right)\left(r,12\right),m=\frac{4}{3}$

F$-4$

G$-1$

H 0

J 3

Short answer

The option G$\left(-1\right)$ represents the required value.

Step-by-step solution

Step 1. Determine the formula that can be used.

The slope formula$m=\frac{y_2-y_1}{x_2-x_1}$can be used to calculate the required value.

Step 2. Take the help of the obtained method.

Take the help of formula for slope of a line represented by $m=\frac{y_2-y_1}{x_2-x_1}$in which the required values can be filled by using the provided points and slope as the points are in the form of $\left(x_1,y_1\right)\left(x_2,y_2\right)$.

$$\begin{gathered} \frac{4}{3}=\frac{12-8}{r-\left(-4\right)} \\ \frac{4}{3}=\frac{4}{r+4} \\ \frac{4}{3}\cdot 3=\frac{4}{r+4}\cdot 3 \\ 4=\frac{12}{r+4} \\ 4\left(r+4\right)=\frac{12}{r+4}\cdot \left(r+4\right) \\ 4r+16=12 \\ 4r+16-16=12-16 \\ 4r=-4 \\ \frac{4r}{4}=\frac{-4}{4} \\ r=-1 \end{gathered}$$

Step 3. Write the conclusion.

The value of r is$-1$ so it is the required value.