Question

Find the equation for the line that passes through the point (0,-1) and that is perpendicular to the line with the equation (y-3)=-3/4(x-1).

Answer 1

I assume you meant    (y-3)=(-3/4)(x-1).  If so, this line has slope -3/4.  A line perpendicular to (y-3)=(-3/4)(x-1) has a slope that is the negative reciprocal of -3/4:  That new slope is +4/3.

The new line is thus y - (-1) = (4/3)(x-0), or   y + 1 = (4/3)x, or

                                                                       y = (4/3)x - 1   (answer)