If an equation represents direct variation, which of the following forms will it take? $$ \begin{array}{l}y=m x+b ext { where } b
eq 0 \ y=x^{2} \ y=k x ext { where } k
eq 0 \ y=\frac{k}{x}\end{array} $$

Question

If an equation represents direct variation, which of the following forms will it take? $$ \begin{array}{l}y=m x+b 	ext { where } b 
eq 0 \ y=x^{2} \ y=k x 	ext { where } k 
eq 0 \ y=\frac{k}{x}\end{array} $$

UpStudy AI · Accepted Answer

An equation represents direct variation if it can be expressed in the form $$ y = kx $$, where $$ k $$ is a non-zero constant. This means that $$ y $$ varies directly with $$ x $$ and there is no constant term added or subtracted (i.e., $$ b = 0 $$).

Let's analyze the options provided:

1. $$ y = mx + b $$ where $$ b 
eq 0 $$: This represents a linear equation but not direct variation because of the non-zero constant $$ b $$.

2. $$ y = x^2 $$: This represents a quadratic relationship, not direct variation.

3. $$ y = kx $$ where $$ k 
eq 0 $$: This is the correct form for direct variation.

4. $$ y = \frac{k}{x} $$: This represents an inverse variation, not direct variation.

Therefore, the correct form that represents direct variation is:

**$$ y = kx $$ where $$ k 
eq 0 $$**.
The correct form for direct variation is $$ y = kx $$ where $$ k 
eq 0 $$.

If an equation represents direct variation, which of the following forms will it
take?

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