Question

Which of the following equations contains the point (8,5) and is perpendicular to the line y=2x-3

Answer 1

y = -
`(1)/(2)` x + 9

Explanation:

The equation of a line in slope- intercept form is

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

y = 2x - 3 ← is in slope- intercept form

with slope m = 2

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

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

y = -
`(1)/(2)` x + c ← is the partial equation

To find c substitute (8, 5) into the partial equation

5 = - 4 + c ⇒ c = 5 + 4 = 9

y = -
`(1)/(2)` x + 9 ← equation of line