Question

What is an equation of the line that passes through the point (8,-8)(8,−8) and is perpendicular to the line 4x-3y=184x−3y=18?

Answer 1

The equation of the line is
`y = -(3x)/(4) - 2`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Perpendicular lines:

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to the line 4x-3y=18

First, we place this line into the format, to find the slope:

`4x - 3y = 18`

`3y = 4x - 18`

`y = (4x)/(3) - 6`

This line has slope 4/3. So, for the perpendicular line, the slope will be of m as such:

`(4m)/(3) = -1`

`4m = -3`

`m = -(3)/(4)`

So the desired line will have an equation in the following format:

`y = -(3x)/(4) + b`

Passes through the point (8,-8)

We use this to find b. This point means that when
`x = 8, y = -8`. So

`y = -(3x)/(4) + b`

`-8 = -(3*8)/(4) + b`

`-8 = -6 + b`

`b = -2`

So

`y = -(3x)/(4) - 2`