Question

Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the orgin

Answer 1

y = -
`(1)/(2)` x

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 8x - 4y = 12 into this form

Subtract 4x from both sides

- 4y = - 8x + 12 ( divide all terms by - 4 )

y = 2x - 3 ← in slope- intercept form

with slope m = 2

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(2)`

Since the line passes through the origin then c = 0

y = -
`(1)/(2)` x ← equation of perpendicular line