Chapter 5.2, Problem 2P

Determine whether each equation represents a direct variation. If it does, find the constant of variation.

$3x+4y=-5$

To determine

To determine if the given equation represents a direct variation.

Answer to Problem 2P

The given equation does not show direct variation.

Explanation of Solution

Given information:

  $3x+4y=-5$

Direct variation means when the given variables always have the same ratio. That is $\frac{y}{x}=k$ , where k is any constant.

Hence when equation is in a direct variation it can be written in form $y=kx$

Now let us check the given equation,

  $\begin{array}{l}3x+4y=-5\\ 4y=-5-3x\\ y=-\frac{5}{4}-\frac{3}{4}x\end{array}$

Hence the given equation does not show direct variation.