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

y = x + 1 has slope 1, so a perpendicular to it will have slope -1
From the general equation for a line you have:
y = -x + b, where b is the intercept, you substitute 3 and -1 in it and you get:

-1 = -3 + b, so b = 2

Your line is y = -x + 2