Question

Solve each equation for y to determine whether x and y show direct variation 9-5x=4y

A) Yes, because the equation is in the form y=mx+b, indicating direct variation.
B) No, because the equation is not in the form y=mx, and the coefficient of x is not a constant.
C) Yes, because the coefficient of x is -5, indicating direct variation.
D) No, because there is a constant term (-9) in the equation, which does not fit the pattern of direct variation.

Answer 1

The equation 9-5x=4y does not represent direct variation because it is not in the form y=mx, and the coefficient of x is not a constant.

Step-by-step explanation:

To determine whether x and y show direct variation in the equation 9-5x=4y, we need to solve the equation for y. First, we isolate the y term by subtracting 9 from both sides of the equation:

9 - 5x = 4y

Next, we divide both sides of the equation by 4:

(9 - 5x) / 4 = y

This equation is not in the form y=mx, and the coefficient of x is not a constant. Therefore, the correct answer is B) No, because the equation is not in the form y=mx, and the coefficient of x is not a constant.