Definition of slope between two points
\(m=\frac{y_2-y_1}{x_2-x_1}\)
With the values we know plugged in
\(\frac{1}2=\frac{r-13}{5-9}\)
5-9 evaluates to -4.
\(\frac{1}2=\frac{r-13}{-4}\)
We could do a number of things from here to solve this.
- Since the bottom multiplies by -2 from the first fraction to the next, so does the top...1 × -2 = -2. Therefore, r-13 = -2. Add 13 to each side to get r = 11.
- Multiply each side by -4. -2 = r-13...see above
- Cross multiply to get 1(-4) = 2(r-13) ⇒ -4 = 2r - 26 ⇒ 22 = 2r ⇒ r = 11
\(\boxed{r=11}\)
