Question

Quiz 8. This one is more challenging: Which equation does NOT represent a direct variation?A y = 12By= -23C62 - y=0Dy+1 = 4x + 1E y +1 = 48ОСODОАOBО Е1244del

Answer 1

An equation that represents a direct variation has the following form:

$y=a\cdot x\text{.}$

Where a is a constant different to zero.

A. This equation represents a direct variation with constant a = 1/3.

B. This equation represents a direct variation with constant a = -2.

C. We rewrite the equation as:

$\begin{gathered} 6x-y=0, \\ 6x=y, \\ y=6x\text{.} \end{gathered}$

We see that this equation represents a direct variation with a constant a = 6.

D. We rewrite the equation as:

$\begin{gathered} y+1=4x+1, \\ y=4x+1-1, \\ y=4x\text{.} \end{gathered}$

We see that this equation represents a direct variation with a constant a = 4.

E. We rewrite the equation as:

$\begin{gathered} y+1=4x, \\ y=4x-1. \end{gathered}$

We see that this equation has an additional constant term. So this equation does not represent a direct variation.

Answer: E