Question

A given line has the equation 2x + 12y = −1.

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

y = (
)x + 9

Answer 1

y = 6x + 9

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 2x + 12y = - 1 into this form

Subtract 2x from both sides

12y = - 2x - 1 ( divide all terms by 12 )

y = -
`(1)/(6)` x -
`(1)/(12)` ← in slope- intercept form

with slope m = -
`(1)/(6)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(6) )` = 6

Note the line crosses the y- axis at (0, 9) → c = 9

y = 6x + 9 ← equation of line