Question

A straight line, L, passes through the point with coordinates (4, 7) and is perpendicular to the line with equation y = 2x + 3. Find an equation of the straight line L.

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)` , then

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

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

7 = - 2 + c ⇒ c = 7 + 2 = 9

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