Looking at the given equation, we can see that its slope is equal to .
y=- 3 ⇔ y= x-3
Therefore, the given line is horizontal. A line perpendicular to a horizontal line must be vertical. We can write a general equation for all lines perpendicular to the given equation.
x=a
We also want the parallel line to pass through the point ( 4,- 6). Therefore, a must be equal to 4.
x= 4
Finally, we can verify our answer by graphing both lines on the same coordinate plane. If they are perpendicular, they will intersect at a right angle.
We can see by looking at the graphs of the functions that they are indeed perpendicular.
