If you are paid a weekly base salary of $200 plus an hourly wage of$5.00, determine an equation...

Question:

If you are paid a weekly base salary of {eq}$200 {/eq} plus an hourly wage of {eq}$5.00 {/eq}, determine an equation for finding your weekly gross pay ({eq}P {/eq}) for {eq}t {/eq} hours.

Specify a number of hours between {eq}25 {/eq} and {eq}50 {/eq} hours worked for {eq}1 {/eq} week and determine your gross pay for that week.

Linear Functions

Linear functions are equations written in some form {eq}f(x) = m*x + b {/eq}, where f(x) is our result, m is our scaling factor (or slope), x is our variable, and b is our initial value (when x = 0). They are called linear because as x increases, f(x) will increase or decrease proportionally, drawing a straight line. An example of a function might be f(x) = 2x + 3. We could substitute any number for x, and f(x) would change in response. If we substituted 5 for x, we would end up with f(x) = 2*5 + 3 = 13.

This question is a great example of a linear function. In this case, we know that our base salary is $200, and for every hour worked, we make an additional$5. We can frame this as a function:

{eq}f(x) = 5*x + 200 {/eq}

The x represents the number of hours worked in a week, and f(x) represents the amount of money we earn. If we work 0 hours a week, we earn:

{eq}f(x) = 5*(0) + 200 = 200 {/eq}

We still earn $200 even without showing up to work, which is really nice. Most people work people 25 and 50 hours a week, however. If we worked a standard workweek of 40 hours, we would just substitute 40 for x, as follows: {eq}f(x) = 5*(40) + 200 {/eq} {eq}f(x) = 200 + 200 {/eq} {eq}f(x) = 400 {/eq} Therefore, if we earned a base salary of$200 per week plus an hourly wage of $5, and we worked 40 hours in a week, we would earn$400.