Question

PLEASEE HELPP!!!!

What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ?

Enter your answer in the box.

Answer 1

y = -
`(1)/(4)` x +
`(15)/(2)`

the equation of a line in slope- intercept form is

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

y = 4x + 5 is in this form with slope m - 4

Given the slope of a line m, then the slope (
`m_(2)`) of a line perpendicular to it is

`m_(2)` = - (1 / m ) = -
`(1)/(4)`

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

to find c, substitute ( 2, 7 ) into the partial equation

7 = -
`(1)/(2)` + c ⇒ c =
`(15)/(2)`

y = -
`(1)/(4)` x +
`(15)/(2)` ← equation of perp. line