Question

Write an equation for the line that passes through (4,-6) and (-7,-6). Is the line parallel or perpendicular to the y-axis?

Answer 1

Answer:

y = -6, perpendicular

Step-by-step explanation:

You can use the points to find the slope of the line:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{-6-(-6)}{-7-4} =\frac{-6+6}{-7-4}=\frac{0}{-11}=0$

Then, using point-slope form, choose one set of coordinates to use for y1 and x1:

$y-y_{1}=m(x-x_{1})$

$y-(-6)=0(x-4)$

$y+6=0$

$y=-6$

Since the slope of the line is zero, it's a horizontal line. The y-axis is a vertical line, which means that the line is perpendicular to the y-axis.