Question

Identify the equation of a line perpendicular

to y = -x - 6 and passing through (1,4)
in slope-intercept form.

Answer 1

y = x + 3

Explanation:

The equation of a line in slope- intercept form is

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

y = - x - 6 ← is in slope- intercept form

with slope m = - 1

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

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

y = x + c ← is the partial equation

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

4 = 1 + c ⇒ c = 4 - 1 = 3

y = x + 3 ← equation of line