What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)?

This is going to be an long answer, so I'm putting the answer first. y=3x-7

First, you have to find the equation of the line given. You can use point slope form for that. You can see that the slope is -1/3, and it goes through (2,2). So, the equation would be
y-2=-1/3(x-2)
Which simplifies to
y=-1/3x+8/3

Now, we can get on to finding the actual answer. The slope of a line perpendicular would be the negative reciprocal of the original slope. That just means you flip it and multiply it by -1. So, the slope of the new line is 3. Now you can use point slope form again and make an equation, which is
y+1=3(x-2)
Which simplifies to
y=3x-7

Please don't ask me why the slope is the negative reciprocal, or how they came up with the formula for the point slope form. I DON'T KNOW. If you want to know so bad you would give up chick-fil-A for the rest of your life, there's always google.