Question

I have no idea how to do this
What is the equation of the line passing through (8, –6) and perpendicular to the line y = x – 2 in slope-intercept form?

Answer 1

We know that the slope of our original equation is 1.
What we need is the equation of a line that is perpendicular to y = x - 2.

The "negative reciprocal" of the slope of our original equation of y=x-2 can be determined by taking the original slope of:
\[\frac{ 1 }{ 1}\]
and then flipping the numerator and the denominator. The amazing thing is this still gives us 1. However, it is the "negative" reciprocal. So, we multiply by -1.

so, the beginning of our new equation is:
\[y = -1 x + b\]

Then, sub in (8, -6) into your new equation:
\[-6=-1(8) + b\]
we find that after solving for b:
b=2
and our final equation is:
y=-x+2

Answer 2

That was very helpful! Thank you so much!