Question

Write the equation of a line that is perpendicular to y=½x - 9 and passes through the point (3, -2).

Answer 1

y = - 2x + 4

Explanation:

the equation of a line in slope- intercept form is

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

y =
`(1)/(2)` x - 9 ← is in slope- intercept form

with slope m =
`(1)/(2)`

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

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

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 2(3) + c = - 6 + c ( add 6 to both sides )

4 = c

y = - 2x + 4 ← equation of perpendicular line