21. Which of the following equations is not an example of a direct variation equation? (Circle your answer) $$ \begin{array}{llll} ext { a. } y=x & ext { b. } y=\frac{1}{4} x & ext { c. } y=5 x-2 & ext { d. } y=9 x\end{array} $$

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21. Which of the following equations is not an example of a direct variation equation? (Circle your answer) $$ \begin{array}{llll}	ext { a. } y=x & 	ext { b. } y=\frac{1}{4} x & 	ext { c. } y=5 x-2 & 	ext { d. } y=9 x\end{array} $$

UpStudy AI · Accepted Answer

A **direct variation** equation is one that can be written in the form $$ y = kx $$, where $$ k $$ is a constant of proportionality. In such equations, $$ y $$ varies directly as $$ x $$, meaning that as $$ x $$ increases or decreases, $$ y $$ does so proportionally without any additional terms.

Let's analyze each option:

- **a. $$ y = x $$**
  
  This fits the form $$ y = kx $$ with $$ k = 1 $$. **Direct variation.**

- **b. $$ y = \frac{1}{4}x $$**
  
  This also fits the form $$ y = kx $$ with $$ k = \frac{1}{4} $$. **Direct variation.**

- **c. $$ y = 5x - 2 $$**
  
  This equation includes an additional constant term ($$-2$$) and cannot be written purely in the form $$ y = kx $$. **Not a direct variation.**

- **d. $$ y = 9x $$**
  
  This fits the form $$ y = kx $$ with $$ k = 9 $$. **Direct variation.**

**Answer:** **c. $$ y = 5x - 2 $$**
The equation $$ y = 5x - 2 $$ is not a direct variation because it includes a constant term.

Which of the following equations is not an example of a direct variation equation? (Circle
your answer)

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