Question

Which equations show a direct variation between x and y when solved for y?Choose all answers that are correct. A -10+y=3x-10B y=-1/8xC y+9=9xD y=4-1

Answer 1

Procedure:

1. Make y the subject of the formula in all the given equations

2.Then compare the relationship between x and y for direct variation.

`\begin{gathered} -10+y=3x-10 \\ \text{Adding 10 to both sides, we get, } \\ y=3x \end{gathered}`

In y = 3x, the variation of y and x is a DIRECT VARIATION.

B:

`y=(1)/(8)x`

The variation of x and y in equation B is DIRECT VARIATION

For the equation in option C, that is,

`\begin{gathered} y+9=9x \\ y=9x-9 \end{gathered}`

The variation in equation C is a DIRECT VARIATION.

But in equation D, y does not vary with x, that is, y has no direct variation with x.

Therefore, the correct answers are options A, B, and C.