Find the value of r so the line that passes through each pair has the given slope.
1. (r,3), (5,9), m=2
Just use the definition of a slope. Say that we have 2 points $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$.
The slope is given by: $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$
Here: $\displaystyle x_1 = r, \ y_1 = 3, \ x_2 = 3, \ y_2 = 9, \ m = 2$
Plug it all in and simply solve.
The gradient of the line, m, is 2. Now remember when we have two points on a line we can find the gradient using this formula:
$\displaystyle m = \frac{y_1 - y_2}{x_1 - x_2}$
$\displaystyle 2 = \frac{3 - 9}{r - 5}$
$\displaystyle \Rightarrow 2(r - 5) = -6$
Now solve for r.