Question

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

y -4 = (x - 6) and passes through the point (-2, -2)?

Answer 1

y = -x - 4

Explanation:

Determine the slope of y -4 = (x - 6).

To do this, compare:

y -4 = (x - 6)

y - k = m(x - h), where m represents the slope of the line.

Here the slope of the given line is 1.

We want the equation of a line perpendicular to the given line, whose slope is 1. The slope of the perpendicular line is then -1/1, or -1 (think: "negative reciprocal").

Now we're ready to write the desired equation in slope-intercept form y = mx + b:

Since this new line passes through (-2, -2), the following is true:

-2 = (-1)(-2) + b. Thus, b = -4, and the desired equation is then

y = -x - 4