Question

Write the equation of the line IN STANDARD FORM that is perpendicular to the line given and through the given point. Do not use spaces in your equation. Y=1/3x-2 (0,4)

Answer 1

3x + y = 4

Explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First step is to obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

given the line with equation

y =
`(1)/(3)` x - 2 ← in slope- intercept form

with slope m =
`(1)/(3)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(3) )` = - 3

the line passes through the y- axis at (0, 4 ), then c = 4

y = - 3x + 4 ← equation in slope- intercept form

add 3x to both sides

3x + y = 4 ← equation of perpendicular line in standard form