Chapter 11.6, Problem 43PPE

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 43PPE

Direct variation, $x=2.5y$ , $8$

Explanation of Solution

Given table:

x	y
10	4
20
_8__	3.2

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 direct variation because in the table the value of x increases then the value of y also increases and vice versa. And x and y both are directly proportional

Equation for the given data in table is

  $\begin{array}{c}x=2.5y\\ ifx=10andy=4\\ thenx=2.5y\\ 10=\left(2.5\right)\cdot 4\\ 10=10\\ iifx=8andy=3.2\\ thenx=2.5y\\ 8=\left(2.5\right)\cdot 3.2\\ 8=8\\ soforx=20\\ x=2.5y\\ 20=2.5y\\ y=\frac{20}{2.5}\\ x=8\end{array}$

x	y
10	4
20	8
_8__	3.2