Question

Give the slope-intercept form of the equation of the line that is perpendicular to –7x + 5y = 12 and contains P(–7, 4).

Select an answer

y = x 

y = x 

y  – 7 = (

x + 4)

y  – 4 = ( x + 7)

Answer 1

y = -
`(5)/(7)` x - 1

the equation of a line in slope-intercept form is

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

rearrange - 7x + 5y = 12 into this form

add 7x to both sides

5y = 7x + 12 ( divide all terms by 5 )

y =
`(7)/(5)` x +
`(12)/(5)` ← in slope- intercept form

with slope m =
`(7)/(5)`

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

perpendicular slope = -
`(1)/(m)` = -
`(5)/(7)`

The partial equation of the perpendicular line is

y = -
`(5)/(7)` x + c

to find c substitute (- 7, 4 ) into the partial equation

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = -
`(5)/(7)` x - 1 ← in slope- intercept form