Question

The weekly salary of a store manager includes a $30 bonus plus the number of hours the manager works multiplied by the managers earnings per hour. Is this situation defined by a linear function?

Answer 1

Yes. The situation is defined by a linear function.

Solution:

Given, The weekly salary of a store manager includes a $30 bonus plus the number of hours the manager works multiplied by the managers earnings per hour.  

Is this situation defined by a linear function?

Yes, the above given situation is defined by a linear function.

Now, let us see the linear equation for above situation

Let the number of hours worked by manager be "x", and cost per hour be "c" and total salary be "y"

Then, total salary is given as,

Total salary = $ 30 bonus + number of hours worked $\times$ cost per hour

$\rightarrow \mathrm{y}=30+\mathrm{x} \times \mathrm{c}\\\\ \rightarrow \mathrm{y}=\mathrm{c} \mathrm{x}+30$

Above equation is a linear equation as "c" is constant ( cost per hour )

Hence, the given situation can be defined by linear function.