Answer :

r=11.  This is because you can use the point slope formula.  y = mx + b.  Plug 9 in for x and 13 in for y.  The slope of 1/2 is m.  You will then find b which is the y-intercept.  Then rewrite the equation as y=1/2x+8.5.  Plug 5 in for x and then simplify the equation.  You will discover that y, which is r, is 11.
RedRicin
Definition of slope between two points
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

With the values we know plugged in
[tex]\frac{1}2=\frac{r-13}{5-9}[/tex]

5-9 evaluates to -4.
[tex]\frac{1}2=\frac{r-13}{-4}[/tex]

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

[tex]\boxed{r=11}[/tex]

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