Chapter 8.3, Problem 41HP

To determine

To calculate: To explain how a linear equation represents a function.

Answer to Problem 41HP

A linear equation is function because for every value of $x$ there is different value of $y$ ,

Explanation of Solution

Given information: Linear equation represents a function

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

As per the definition of function, if no input has more than one output, then it is referred to as function.

And since in case of a linear equation, for every value of $x$ there is different value of $y$ , thus linear equation represents a function

Different ways of real-world representation of linear function are :

• Graph
• Table
• Word form
• Function notation