Chapter 1.6, Problem 38HP

To determine

To describe: a real time example that can be represented using relation. Also, to explain the dependencies and represent the relation in 3 different ways

Explanation of Solution

Example:

An electrician charges a base fee of $70 plus $50 for each hour of work

Let, x be the hours of work

y be the amount charged by the electrician.

Hence, according to the example the relation is: $y=70+50x$

Now, y will be dependent on the variable x because the more the number of hours the electrician works, the more he will charge for the work done in that amount of time.

Calculation of Graph:

No. of hours of work ( x )	Amount charged by electrician ( y )
0	$70
1	$120
1.2	$130
2	$170

By taking different values of hours of work, the graph can be plotted.

Graph:

  

Interpretation:

The above graph represents a linear relation.

Representation of relation:

1^sttype: (Co-ordinate system)

Let R be the relation in terms of ordered pairs.

R = {(0, 50),(1, 120),(1.2, 130),(2, 170),……so on}

2^ndtype: Mapping

  

3^rdtype: Tabular form

No. of hours of work ( x )	Amount charged by electrician ( y )
0	$70
1	$120
1.2	$130
2	$170