find the equation of a line perpendicular to −4x+4y=4 that contains the point (−4,5).

(write the equation in slope-intercept form.)

y = - x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Rearrange - 4x + 4y = 4 into this form by adding 4x to both sides

4y = 4x + 4 ( divide all terms by 4 )

y = x + 1 ← in slope- intercept form

with slope m = 1

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

= - = - = - 1, thus

y = - x + c ← is the partial equation

To find c substitute (- 4, 5) into the partial equation

5 = 4 + c ⇒ c = 5 - 4 = 1

y = - x + 1 ← equation of perpendicular line