Chapter 4.1, Problem 62HP

To determine

To Graph:

Draw a graph representing a real-world linear function and write an equation for the graph. Describe what the graph represents.

Explanation of Solution

Formula Used:

Equation of slope-intercept form of a line is given by:

  $y=mx+b\mathrm{............................}(1)$

Where

  $\begin{array}{l}b=y-\mathrm{int}ercept\\ m=\frac{rise}{run}=slope\end{array}$

Calculation:

Let us assume:

The cost of a tour is $2 and guide fee is $1 per person. Then , we can represent the total tour cost C , for p persons as follows:

Let

C = Total tour cost

p = Total number of persons

b = Tour cost = $2

m =Guide cost per person = $1

Then , we have

Guide cost per person = $1

Guide cost for p persons = $ p

Tour cost = $2

Total tour cost = $p+2$

So, we can represent the given situation in slope-intercept form for the total tour cost C , for p persons:

  $C=p+2$

Graph:

The C -intercept is 2

So, first we plot the point (0,2) on the graph . Then we go 1 unit up (rise) and then go 1 unit to the right (run) , since the slope is 1 , and plot the point (1,3). Now join the two points , we have the required graph .