Question

Find the equation of the line that is

perpendicular to the line y = 2x + 3 and
passes through the point (6, 4).

Answer 1

y = -
`(1)/(2)` x + 7

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

y = 2x + 3 ← 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)` , then

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

to find c, substitute the point (6, 4 ) for x and y into the partial equation

4 = -
`(1)/(2)` (6) + c = - 3 + c ( add 3 to both sides )

7 = c

y = -
`(1)/(2)` x + 7 ← equation of perpendicular line