Chapter 6, Problem 12CT

To determine

To determine and graph a linear inequation.

Explanation of Solution

Given:

All the items cost $1 or $5

Spend less than $45

Let’s consider $x$ be the items cost $1 and $y$ be the items cost $5

Then the equation of inequality is,

  $\Rightarrow x+5y<45$

Converting into slope- interception form,

  $\Rightarrow y<-\frac{1}{5}x+9$

The slope is $-\frac{1}{5}$ and $y$ intercept is $9$ .

Graph:

  

The shaded region gives the solution of $x+5y<45$ and $x$ and $y$ are positive.

Interpretation:

Therefore, the above graph defines solution of $x+5y<45$ .