Determine whether each pair of lines is parallel, perpendicular, or neither

Question

X+4y=8 and 4x-y=8

Answer 1

Hi Sofia,

 

A question like is easily answered once you determine the slope of the line.

1. Lines that have the same slope are parallel.
2. Lines whose slopes are the negative reciprocal of each other (e.g. 1/2 and -2) are perpendicular.
3. All other lines are neither.

 

The most thorough way to determine the slope to a line is to put the formula for it in the y=mx + b form, where m (the coefficient in front of the x) is the slope.

 

When you do that with the two lines you gave us, you will get a slope of negative 1/4 for the first line and 4 for the second line.  These two numbers are negative reciprocals of each other, so the lines are perpendicular.