Question

Indicate whether the lines are parallel, perpendicular, or neither. Justify your

answer.
a. Y = −3x − 1 and 12x = 4y + 7
b. X− 7y= 10 and 2x+ 14y= 21

Answer 1

Lines are parallel when they have the same slope. Example: 2x-1 and 2x+3 would be parallel.

Lines are perpendicular when their slopes are negative reciprocals of each other. Example: 4/3x+3 and -3/4x-7 would be perpendicular.

As for your question-

In order to find the slope of a line in these problems we can put it into y=mx+b form.
12x=4y+7
-4y=-12x+7
y=3x-7/4
The slopes are not the same so the answer is neither.

-7y=-x+10
y=1/7x-10/7

14y=-2x+21
y=-1/7x+3/2
Slopes aren’t the same so neither.

You can check on a graphing calculator too.