Question

What is the equation in slope-intercept form of the line that passes through the

point (2,-2) and is perpendicular to the line represented by y = x +2?

Answer 1

`y=-x`

Explanation:

The slope-intercept form of a line can be written as
`y=mx+b`, where
`m` is the slope,
`b` is the y-intercept, and
`(x,y)` are the coordinates of any point that this line passes through.

Perpendicular lines have negative-reciprocal slopes. Therefore a line perpendicular to
`y=x+2` will have a slope of
`-(1)/(1)=-1`.

Now that we have a slope and coordinates of a point that the line passes through, we can solve for the y-intercept and the equation of the line:

`-2=-1(2)+b, \\b=0`

Thus, the equation of this line is
`\fbox{$y=-x$}`.