Chapter 11.6, Problem 44PPE

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 44PPE

Direct variation, $70x=y$ , $0.9$

Explanation of Solution

Given table:

x	y
0.4	28
1.2	84
___	63

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

  $\begin{array}{c}70x=y\\ ifx=0.4andy=28\\ then70x=y\\ 70\cdot \left(0.4\right)=28\\ 28=28\\ ifx=1.2andy=84\\ then70x=y\\ 70\cdot \left(1.2\right)=84\\ 84=84\\ sofory=63\\ 70x=y\\ 70x=63\\ x=\frac{63}{70}\\ x=0.9\end{array}$

x	y
0.4	28
1.2	84
0.9	63