Q3. - Algebra 1

Question

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

$\mathit{x}\mathit{y}\mathbf{=}\mathbf{4}$

Step-by-Step Solution

Answer

The equation 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.

The relationship of the form $xy=k$ is known as inverse variation. Comparing the given equation $xy=4,xy=k$, observe that $k=4$, therefore, the product is constant so the equation represents the inverse variation.

Step 3. Check for direct variation.

The relationship of the form $y=kx$ is known as direct variation. Observe that the given equation $xy=4$ is not comparable with $y=kx$ i.e., the product is not constant so the equation doesn’t represent the direct variation.