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)