Q9. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

 

A direct variation can be represented by an equation of the form $k=xy$, where k is a nonzero constant.

Step-by-Step Solution

Answer

The given statement is False.

A corrected statement is “A inverse variation can be represented by an equation of the form $xy=k$, where k is a nonzero constant.”

Step 1. State the concept of direct variation.

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

Step 2. Explanation of the statement.

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.

 

Therefore, the given statement “A direct variation can be represented by an equation of the form $xy=k$, where k is a nonzero constant.” defines the inverse variation and not direct variation.

Step 3. Write whether the statement is true or false.

So, the given statement is false. And the correct statement is “An inverse variation can be represented by an equation of the form $xy=k$, where k is a nonzero constant.”