Chapter 11.6, Problem 47PPE

To determine

Pedro says that the graph represents an inverse variation. Is he correct? Explain.

Answer to Problem 47PPE

No.

Explanation of Solution

Given Information:

While graphing a certain function, Pedro sees that the value of y decreases by 2 whenever the value of x increases by 1.

Concept Used:

• Mathematically relationship between two variables that can be expressed by an equation in which one variable is equal to constant times the other variable is called direct variation.
• Mathematically relationship between two variables that can be expressed by an equation in which the product of two variable is constant is called inverse variation.

Calculation:

According to question the value of y decreases by 2 whenever the value of x increases by 1.

Pedro is incorrect because in inverse variation the product of two variables always remains constant but in this case it is no constant.

For example

  $\begin{array}{c}letx=5andy=3\\ xy=k\\ 5\cdot 3=k\\ 15=k\\ butthevalueofydecreasesby2wheneverthevalueofxincreasesby1.\\ sox=5+1\\ x=6\\ andy=3-2\\ y=1\\ xy=6\cdot 1\\ xy=6\\ whichisnotequalto15\end{array}$

So Pedro is incorrect, it is not a inverse variation.