Chapter 5.4, Problem 26MCQ

To determine

Write and graphically represent the equation of given salesperson’s earnings and draw inference about independent and dependent variable used.

Answer to Problem 26MCQ

Required Equation: $y=18x+75$

Independent variable here shows the total number of hours worked by the salesperson.

The dependent variable here shows the total earnings of the salesperson.

Explanation of Solution

Given Information Earnings per hour of salesperson = $18 and bonus = $75

For the given practical problem, we are required to frame a function,

Let   $f(x)=18x$ where, x = earnings per hour, but, clearly stated that, $75 bonus is also provided.

So, our final equation becomes

  $y=18x+75$

We need to plot the above equation graphically.

Calculation

(i) For 1^st point

Let the salesperson started working,

at $x=0$ hrs

So, $y=18x+75$

  $=(18\times 0)+75(\text{for}x=0\text{hrs})$

  $y=75$

  $x=0\text{and }y=75$

(ii) For 2^nd point

Let, $x=2$

So, $y=18x+75$

  $\begin{array}{l}=(18\times 2)+75\\ =36+75=111\end{array}$

  $x=2\text{and }y=111$

Graph Plotting

  

Conclusion

• Independent variable here shows the total number of hours worked by the salesperson.
• The dependent variable here shows the total earnings of the salesperson.