Question

find the equation of the line that contains the point p(4, 5) and is perpendicular to the graph of y = 5/4 x − 1.

Answer 1

y = -
`(4)/(5)` x +
`(41)/(5)`

Explanation:

the equation of a line in slope- intercept form is

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

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

with slope m =
`(5)/(4)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((5)/(4) )` = -
`(4)/(5)` , then

y = -
`(4)/(5)` x + c ← is the partial equation of the perpendicular line

to find c substitute (4, 5 ) into the partial equation

5 = -
`(16)/(5)` + c ⇒ c = 5 +
`(16)/(5)` =
`(25)/(5)` +
`(16)/(5)` =
`(41)/(5)`

y = -
`(4)/(5)` x +
`(41)/(5)` ← equation of perpendicular line