Question

the slope-intercept form of an equation of the line perpendicular to the graph of x – 3y = 5 and passing through (0, 6).

Answer 1

y = - 3x + 6

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange x - 3y = 5 into this form

Subtract x from both sides

- 3y = - x + 5 ( divide all terms by - 3 )

y =
`(1)/(3)` x -
`(5)/(3)` ← 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

Note the line crosses the y- axis at (0, 6) ⇒ c = 6

y = - 3x + 6 ← equation of perpendicular line