Question

Find a if the point (3,a) is on the line that passes through (-2,7) and (5,-3).

Answer 1

Your first step is to find the slope of the line. You can find that using the formula $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Plug the x- and y- values from the coordinate pairs into the formula.
 
$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$   Plug in the coordinates
$\frac{-3 - 7}{5 - (-2)}$   Cancel out the double negative
$\frac{-3 - 7}{5 + 2}$   Add and subtract
$\frac{-10}{7}$

Next, you can use the same formula to find a by setting it against the slope you just found.

slope = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$   Plug in the values
$\frac{-10}{7}$ = $\frac{7 - a}{-2 - 3}$   Subtract
$\frac{-10}{7}$ = $\frac{7 - a}{-5}$   Multiply both sides by 7
-10 = $\frac{7(7 - a)}{-5}$   Use the Distributive Property
-10 = $\frac{49 -7a}{-5}$   Multiply both sides by -5
50 = 49 - 7a   Subtract 49 from both sides
1 = -7a   Divide both sides by -7
$-\frac{1}{7}$ = a   Switch the sides to make it easier to read
a = $-\frac{1}{7}$