Your first step is to find the slope of the line. You can find that using the formula [tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]. Plug the x- and y- values from the coordinate pairs into the formula.
[tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex] Plug in the coordinates
[tex] \frac{-3 - 7}{5 - (-2)} [/tex] Cancel out the double negative
[tex] \frac{-3 - 7}{5 + 2} [/tex] Add and subtract
[tex] \frac{-10}{7} [/tex]
Next, you can use the same formula to find a by setting it against the slope you just found.
slope = [tex] \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex] Plug in the values
[tex] \frac{-10}{7} [/tex] = [tex] \frac{7 - a}{-2 - 3} [/tex] Subtract
[tex] \frac{-10}{7} [/tex] = [tex] \frac{7 - a}{-5} [/tex] Multiply both sides by 7
-10 = [tex] \frac{7(7 - a)}{-5} [/tex] Use the Distributive Property
-10 = [tex] \frac{49 -7a}{-5} [/tex] Multiply both sides by -5
50 = 49 - 7a Subtract 49 from both sides
1 = -7a Divide both sides by -7
[tex]-\frac{1}{7} [/tex] = a Switch the sides to make it easier to read
a = [tex]-\frac{1}{7} [/tex]
