Question

First using point slope form, write the equation of the line in slope-intercept form

that is perpendicular to y = -3/2 x - 1 and through (9,-2)​

Answer 1

y =
`(2)/(3)` x - 8

Explanation:

The equation of a line in slope- intercept form is

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

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

with slope m = -
`(3)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(2) )` =
`(2)/(3)`

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m =
`(2)/(3)` and (a, b) = (9, - 2), thus

y - (- 2) =
`(2)/(3)`(x - 9), that is

y + 2 =
`(2)/(3)`(x - 9) ← in point- slope form

Distribute right side and rearrange

y + 2 =
`(2)/(3)` x - 6 ( subtract 2 from both sides )

y =
`(2)/(3)` x - 8 ← in slope- intercept form