Are the lines with equations 2x = 8 and -3y = 15 parallel, perpendicular or neither

Expert Answers
hala718 eNotes educator| Certified Educator

Given the equation of the lines:

-3y = 15

2x = 8

Let us rewrite the equations:

==> y= -5

==> x = 4

The line y= -5 is a line parallel to the x-axis and passes through y= -5.

The line x= 4 is a line parallel to the y-axis and passes through x=4.

But we know that the x-axis and the y-axis are perpendicular.

Then the lines -3y=15 and the line 2x=8 are perpendicular.

justaguide eNotes educator| Certified Educator

The line 2x = 8 or x = 4 is one that is parallel to the y-axis. The slope of the line is infinity. -3y = 15 or y = -5 is parallel to the x- axis. This line has a slope equal to 0.

As the x-axis and the y-axis are perpendicular the given lines are perpendicular too.

The given lines 2x = 8 and -3y = 15 are perpendicular.