Question

What is the equation of the line in slope-intercept form that passes through the point (3, –1) and is perpendicular to the line y = x + 1?

Answer 1

To get the equation of a line that's perpendicular to another line, you need to transform the equation you have in the form y=mx+b1 into y=(-1/m)x+b2. So with y=x+1 we know that m=1 and b1=1. Doing the transformation you get:
y=(-1/1)x+b2 or y=-x+b2
To find b2, plug in the point you are given:
-1=(-1)(3)+b2 and solving you get: b2=2
Then you're left with y=-x+2. And in point-slope form (y-y1)=m(x-x1)
you just use the point you were given and you get y+1=-1(x-3).

You don't have to find b to come up with the answer but it's helpful when trying to visualize it. Remeber: m=slope, b=y-intecept.