The line that passes thru (3, -1) and perpendicular to the line y = x + 1 will have the equation of

y = -x + b

(the slope of the given line is m=1 and that of the second line is m=-1. The product of the 2 perpendicular lines is -1)

Substituting (3, -1) into y = -x + b to find b,

-1 = -3 + b

b = 2

Thus the equation is

y = -x + 2

Perpendicular line have slpoes that are negative reciprocals. Did your question get cut off? Perpendicular to what?

In slope-intercept form y = mx + b, the coefficient of x is the slope (m). So if the slope were say, 2, a perpendicular line would have a slope of -1/2. Substitute 3 for x and -1 for y and solve for b.

y - (-1) = k(x-3)

==> y = kx - 3k -1