Question

What is anequation of the line that passes through the points (-6,3) and(-6, -3)?

Answer 1

Recall that the formula for finding the equation of a line that passes through two points is given as

$\begin{gathered} \frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{y-y_1}{x-x_1}\text{ } \\ \text{where (x}_1,y_1)\text{ and (x}_2,y_2)\text{ are the two given points} \end{gathered}$

Thus, let (-6, 3) be (x1, y1) and let (-6, -3) be (x2, y2)

Then by substitution, we have

$\begin{gathered} \frac{-3-3}{-6-(-6)}\text{ = }\frac{y-3}{x-(-6)} \\ \text{This simplifies to} \\ \frac{-6}{0}=\text{ }\frac{y-3}{x+6} \\ \text{Hence, we have } \\ x\text{ + 6 = -6} \\ x\text{ = -6-6} \\ x\text{ = -12} \end{gathered}$