Question

Through: (-9, 0), perpendicular to
y = 3x - 2
In slope intercept form

Answer 1

The equation perpendicular to y = 3x - 2 and passing through (-9, 0) in the slope-intercept form will be:

• 
  `\:\:y\:=-(1)/(3)x-3`

Explanation:

The slope-intercept form of the line equation

`y = mx+b`

where

• m is the slope

• b is the y-intercept

Given the line

y = 3x - 2

comparing with the slope-intercept form of the line equation

The slope of the line y = 3x - 2 is: m = 3

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 3

Thus, the slope of the the new perpendicular line = – 1/m = -1/3 = -1/3

The point-slope form of the line equation is:

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

In our case:

• m = -1/3

• (x₁, y₁) = (-9, 0)

now substituting the perpendicular slope m = -1/3 and (-9, 0) in the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

`y-0=-(1)/(3)\left(x-\left(-9\right)\right)`

`y=-(1)/(3)\left(x-\left(-9\right)\right)`

`y=-(1)/(3)\left(x+9\right)`

`\:\:y\:=-(1)/(3)x-3`

Therefore, the equation perpendicular to y = 3x - 2 and passing through (-9, 0) in the slope-intercept form will be:

• 
  `\:\:y\:=-(1)/(3)x-3`