Respuesta :
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
[tex]\begin{gathered} \text{Simplify it in }\frac{y}{x} \\ \text{Divide equation by x} \\ \frac{3y}{x}=\frac{4x}{x}+\frac{1}{x} \\ \frac{y}{x}=\frac{4}{3}+\frac{1}{3x} \\ \frac{y}{x}\ne\text{ any constant term} \end{gathered}[/tex]So, it does not represent direct variation.
2) 3x = -4y
[tex]\begin{gathered} \text{Simplify it in }\frac{y}{x} \\ 3x=-4y \\ \text{Divide by 3y} \\ \frac{3x}{3y}=\frac{-4y}{3y} \\ \frac{x}{y}=-\frac{4}{3} \\ \frac{y}{x}=-\frac{3}{4} \\ \frac{y}{x}=Cons\tan t\text{ term} \end{gathered}[/tex]It represent direct variation.
3) y + 3x =0
[tex]\begin{gathered} \text{Simplify it in }\frac{y}{x} \\ \text{Divide by x} \\ \frac{y}{x}+\frac{3x}{x}=0 \\ \frac{y}{x}=-3 \\ \frac{y}{x}=\text{ Constant term} \end{gathered}[/tex]It represnt the direct variation.
Answer: 2) 3x = -4y
3) y + 3x = 0
