Question

Write the equation of the line perpendicular to y= -1/2x - 5 through the point (1,-4)

Answer 1

y = 2x - 6

Explanation:

The equation of a line in slope- intercept form is

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

y = -
`(1)/(2)` x - 5 ← is in slope- intercept form

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

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

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

y = 2x + c ← is the partial equation of the line

To find c substitute (1, - 4) into the partial equation

- 4 = 2 + c ⇒ c = - 4 - 2 = - 6

y = 2x - 6 ← equation of line