Question

Tell whether each equation represents a direct variation. If so, identify the constant of variation.

Answer 1

The variation of the equation is ; y/x

if y/x = k , where k is constant then the variation is Constant

1) 3y = 4x+1

`\begin{gathered} \text{Simplify it in }(y)/(x) \\ \text{Divide equation by x} \\ (3y)/(x)=(4x)/(x)+(1)/(x) \\ (y)/(x)=(4)/(3)+(1)/(3x) \\ (y)/(x)\\e\text{ any constant term} \end{gathered}`

So, it does not represent direct variation.

2) 3x = -4y

`\begin{gathered} \text{Simplify it in }(y)/(x) \\ 3x=-4y \\ \text{Divide by 3y} \\ (3x)/(3y)=(-4y)/(3y) \\ (x)/(y)=-(4)/(3) \\ (y)/(x)=-(3)/(4) \\ (y)/(x)=Cons\tan t\text{ term} \end{gathered}`

It represent direct variation.

3) y + 3x =0

`\begin{gathered} \text{Simplify it in }(y)/(x) \\ \text{Divide by x} \\ (y)/(x)+(3x)/(x)=0 \\ (y)/(x)=-3 \\ (y)/(x)=\text{ Constant term} \end{gathered}`

It represnt the direct variation.

Answer: 2) 3x = -4y

3) y + 3x = 0