# Job Salaries

## Overview

John Aggin is offered a position at Microrough and Orange Inc. Both of these are technology companies and are competition to each other. John Aggin wants to find a job that is most suitable for him and would have a higher pay by the end of the year. Microrough will pay a bonus every year (fixed cost) of \$500 plus \$1280 per year. Orange Inc. will pay 1600 per month with no bonus (fixed cost).

## Variables

The independent variable is the time in months.

The dependant variable is the salary (\$) earned.

## Microrough

To find which job offer is better, we must convert the given data into slope/intercept form, standard form, graph or create a table of values and see which plan is better for each situation. In this case, John has done all four processes.
1. Table of Values
2. Slope/y - intercept form

We can find the slope by subtracting two consecutive numbers from the graph above.

So we can pick 1780 and 500.

1780 - 500

= 1280

therefore, m = 1280

The y-intercept would be the value where the x co-ordinate is 0, and looking at the table of values, it seems that it is 500.

Therefore the equation in slope/y-intercept form would be y = 1280x + 500.

3. Standard form

For standard form we would need to have all of the equation from the slope/y-intercept form on one side.

y = 1280x + 500

0 = 1280x - y + 500

1280x - y + 500 = 0

Therefore the equation in standard form is 1280x - y + 500 = 0

4. Graph

There is a linear systems graph all the way down in Point of Intersection. It has both Microrough's and Orange Inc. lines on it.

## Orange Inc.

1. Table of Values
2. Slope/y - intercept form

We can find the slope by subtracting two consecutive numbers from the graph above.

So we can pick 3200 and 1600.

3200 - 1600

= 1600

therefore, m = 1600

The y-intercept would be the value where the x co-ordinate is 0, and looking at the table of values, it seems that it is 0 (origin)

Therefore the equation in slope/y-intercept form would be y = 1600x + 0 or just y = 1600x.

3. Standard form

For standard form we would need to have all of the equation from the slope/y-intercept form on one side.

y = 1600x + 0

0 = 1600x - y + 0

1600x - y + 0 = 0 or 1600x - y = 0

Therefore the equation in standard form is 1600x - y + 0 = 0 or 1600x - y = 0.

4. Graph

As mentioned above, graph will be on Point of Intersection which is down below.

## Point of Intersection (POI)

To find out point of intersection, we must either use equations or use he graph. In this case since it is hard to find the point of intersection using the graph, John used equations.

1. Equations:

the two equations are y = 1280x + 500 and y = 1600x. Since y is common in both equations, the equation can also be written as 1280x + 500 = 1600x. Now we would have to solve for x.

1280x + 500 = 1600x

500 = 1600x - 1280x

500 = 320x

500/320 = x

x = 500/320

Next we need to figure out the y co-ordinate. To this we will have to substitute the x value in any one of the equations. John used y = 1600x.

y = 1600x

y = 1600(500/320)

y = 2500

Now that we have our x and y co-ordinates, the point of intersection would be (500/320, 2500) or in decimal format, (1.5625, 2500).

2. Graph

For the graph method, it is hard to see on this graph but it would also say (500/320, 2500)

***Note: Blue line is Orange Inc. and Purple is Microrough.

## Summary

Both jobs will offer the same amount after approximately one and a half months but late, Orange Inc. will pay John higher.

## Final Verdict

John Aggin should go for Orange Inc. offer because even though the pay is lower in the beginning it will gradually increase at a higher rate and by the end of the year pay more.

## Significance of Solution

This whole project evaluates how to choose the right job when looking at company pays and graphs and tables can be applied in real life when this situation occurs.