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 = \(-\frac{1}{7}\)
