What is the equation of the line that passes through the point (-5,5) and has a
slope of -1?

y = - x

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 )

Here m = - 1 , then

y = - x + c ← is the partial equation

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

5 = 5 + c ⇒ c = 5 - 5 = 0

y = - x ← equation of line

you can't solve x because it is 2 linear equation and you only have one equation

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c