find the value of r so the line that passes through the pair of points has the given slope. (3, 5), (-3, r)…

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, $(x_1,y_1)=(3,5)$ and $(x_2,y_2)=(-3,r)$, and $m = \frac{3}{4}$. So, $\frac{3}{4}=\frac{r - 5}{-3 - 3}$.

Step2: Simplify the denominator

$-3-3=-6$. The equation becomes $\frac{3}{4}=\frac{r - 5}{-6}$.

Step3: Cross - multiply

Cross - multiplying gives $3\times(-6)=4\times(r - 5)$. So, $-18 = 4r-20$.

Step4: Solve for $r$

Add 20 to both sides of the equation: $-18 + 20=4r-20 + 20$. $2 = 4r$. Divide both sides by 4: $r=\frac{2}{4}=\frac{1}{2}$.

Answer:

$r=\frac{1}{2}$