Question

Find the equation of the line which passes through the point (5, 3), and is perpendicular to the line with the equation y = -1/3x-1/3. Express your answer in slope-Intercept form. Simplify your answer

Answer 1

y = 3x - 12

Explanation:

the equation of a line in slope- intercept form is

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

given the line with equation

y = -
`(1)/(3)` x -
`(1)/(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 , then

y = 3x + c ← is the partial equation of the perpendicular line

to find c, substitute the point (5, 3 ) for x, y into the partial equation

3 = 3(5) + c = 15 + c ( subtract 15 from both sides )

- 12 = c

y = 3x - 12 ← equation of perpendicular line