Answer the following: 21. Are the following equations parallel, perpendicular or neither?
-3x + y = -4
x + 3y = 6

As the product of the slop of both lines is -1.

Therefore, the given equations are perpendicular.

Step-by-step explanation:

Given the equations

The slope-intercept form of the equation is

where m is the slope and b is the y-intercept.

Writing both equations in the slope-intercept form

So by comparing with the slope-intercept form we can observe that

slope of equation = 3

i.e.

also

So by comparing with the slope-intercept form we can observe that

the slope of equation = -1/3

i.e.

as

The slope of the perpendicular line is basically the negative reciprocal of the slope of the line.

so

The slope is the negative reciprocal of the slope

Also, the product of two perpendicular lines is -1.

i.e.

VERIFICATION:

It is clear that the product of the slop of both lines is -1.

Therefore, the given equations are perpendicular.