Q2. - Algebra 1

Question

Determine whether each table or equation represents an inverse or a direct variation. Explain.

$x$	1	2	3	4
$y$	24	12	8	6

Step-by-Step Solution

Answer

The table represents an inverse variation.

Step 1. State the concept of direct variation and inverse variation.

The relationship of the form $y=kx$ is called direct variation.

Relationship of the form $xy=k$ or $y=\frac{k}{x}$ where $x,y\ne 0$ for some nonzero constant $k$ is known as inverse variation i.e., $y$ varies inversely as $x$.

Step 2. Check for inverse variation.

Find $xy$ each ordered pair from the table and get,

$$\begin{gathered} 1\cdot 24=24 \\ 2\cdot 12=24 \\ 3\cdot 8=24 \\ 4\cdot 6=24 \end{gathered}$$

The product is constant so the table represents an inverse variation.

Step 3. Check for direct variation.

Find $\frac{y}{x}$ each ordered pair from the table and get,

$$\begin{gathered} \frac{24}{1}=24 \\ \frac{12}{2}=6 \\ \frac{8}{3}=2.67 \\ \frac{6}{4}=1.5 \end{gathered}$$

Since $\frac{y}{x}$ is not constant for any given values of $x$ and $y$, so the table doesn’t represent the direct variation.