For each equation, determine whether it represents a direct variation, an inverse variation, or neither. find the constant of variation when one exists and write it in simplest form.

Direct variation is written in the form y = k * x or x = y * k. And, inverse variation is written in the form y = k/x or x = y/k.

For the first problem, if we isolated the y, we would get:

4y = 3x - 1

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

This is written as y = mx + b, which isn’t the form of direct or inverse variation, so the answer is NEITHER.

For the second equation, we could divide by 2 on both sides to isolate x and see if it is in the correct form:

x = 4/y

This is inverse form, so the second question is INVERSE with a constant of variation as 4.