Chapter 11.6, Problem 45PPE

To determine

Tell whether the given table represents a direct variation or an inverse variation.

Write an equation to model the data. Then complete the table.

Answer to Problem 45PPE

Inverse variation, $xy=48$ , $0.5$

Explanation of Solution

Given table:

x	y
1.6	30
4.8	10
___	96

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 variables is constant is called inverse variation.

Calculation:

The given table represents an inverse variation because x and y both are inversely proportional, if the value of x increases then the value of y decreases and vice versa.

Equation for the given data in table is

  $\begin{array}{c}xy=48\\ ifx=1.6andy=30\\ thenxy=\left(1.6\right)\cdot 30=48\\ ifx=4.8andy=10\\ thenxy=\left(4.8\right)\cdot 10=48\\ sofory=96\\ xy=48\\ x\cdot 96=48\\ x=\frac{48}{96}\\ x=0.5\end{array}$

x	y
1.6	30
4.8	10
0.5	96