Question

What is the equation of the line passing through (2, –2) and perpendicular to the line y = –x + 3 in slope-intercept form?

Answer 1

y = -x . Same slope, plug in x = 2, you get -2 = y.

Answer 2

\[y-yo=m(x-xo)\]
Using it on the line you gave
\[y-0=-1(x-3)\]
so you know the m (slope) is equal to -1
Replacing to the point you want:
\[y+2=-1(x-2)\]
\[y+2=-x+2\]
\[y+x=0\]

Answer 3

You should memorize this rule. two lines are perpendicular if
slope of line1 = m and the slope of line2= -1/m

Also, they are parallel if they have the same slope m.
In your case, m= -1, so the slope of the 2nd line is -1/-1 = 1

Answer 4

Once you know the slope, use Luis... formula
(y -y0) = m(x-x0) where (x0,y0) is any point on your line. In your case (2,-2)

Answer 5

Finally, put it into slope-intercept form
y= mx+b