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} (y_2-y_1)/(x_2-x_1)\text{ = }(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} (-3-3)/(-6-(-6))\text{ = }(y-3)/(x-(-6)) \\ \text{This simplifies to} \\ (-6)/(0)=\text{ }(y-3)/(x+6) \\ \text{Hence, we have } \\ x\text{ + 6 = -6} \\ x\text{ = -6-6} \\ x\text{ = -12} \end{gathered}`