Question

Write the equation in slope-intercept form of the line that passes through

(12,9) and is perpendicular to the graph of y = -3/4x + 1.

Answer 1

We conclude that the equation in slope-intercept form of the line that passes through (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

• 
  `y=(4)/(3)x-7`

Explanation:

We know 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 = -3/4x + 1

comparing with the slope-intercept form of the line equation

The slope = m = -3/4

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 = -3/4

Thus, the slope of the new perpendicular line = – 1/(-3/4) = 4/3

Using the point-slope form

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

where m is the slope of the line and (x₁, y₁) is the point

substituting the values of the slope = 4/3 and the point (12, 9)

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

`y-9=(4)/(3)\left(x-12\right)`

Add 9 to both sides

`y-9+9=(4)/(3)\left(x-12\right)+9`

`y=(4)/(3)x-16+9`

`y=(4)/(3)x-7`

Therefore, we conclude that the equation in slope-intercept form of the line that passes through (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

• 
  `y=(4)/(3)x-7`