Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

2x + 4y = -6; (2,5)

Answer 1

y = 2x + 1

Explanation:

the equation of a line in slope- intercept form is

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

rearrange 2x + 4y = - 6 into this form

subtract 2x from both sides

4y = - 2x - 6 ( divide all terms by 4 )

y = -
`(1)/(2)` x -
`(3)/(2)` ← in slope-intercept form

with slope m = -
`(1)/(2)`

the slope of the perpendicular line is the negative reciprocal of m

`m_(perpendicular)` = 2

y = 2x + c ← is the partial equation

to find c substitute (2, 5) into the partial equation

5 = 4 + c ⇒ c = 5 - 4 = 1

y = 2x + 1 ← equation of perpendicular line