Question

Consider the line -4x-3y=-7.

What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line?

Slope of a perpendicular line:

Slope of a parallel line:

Answer 1

first get it into slope intercept form: y=mx+b m is slope and b is the y intercept

-4x-3y=-7
get y by it’s self
-3y=4x-7
divide by -3
y=-4/3x-7/3
so the of the original line is -4/3

the parallel line has the same slope so the parallel slope is -4/3
the perpendicular slope is opposite reciprocal of the original so it is 3/4

Answer 2

Parallel:
`-\frac43`

Perpendicular:
`\frac34`

Explanation:

Hello!

First, we need to find the slope of the given line. Convert it into Slope-Intercept Form.

Slope - Intercept Form:
`y = mx + b`

Convert

• 
  `-4x - 3y = -7`
• 
  `-3y = 4x - 7`
• 
  `y = -\frac43x + \frac73`

Parallel Lines

Parallel lines have the same slope but an altered y-intercept. Therefore, the slope of the line parallel to this one is also
`-\frac43`.

Perpendicular Lines

Perpendicular lines have an opposite reciprocal slope. That means you flip the sign (+/-) and flip the numerator and denominator. The slope of the line perpendicular to this one is
`\frac34`.