# Fifa 15 Career Mode Season

## The Situation

Bob wants to test his skill in a Career mode season on Fifa 15. He decides that the best way to do this is to play one season on Amateur difficulty, and one season on Beginner difficulty. He will play a 42 game season and record his goal differential on each difficulty level. He decides to record his results in a table and then make a scatter plot with a line of best fit. To challenge himself further, he asks his brother Tom to play the first 10 games of each season. Next, to make it easier to graph his results, Bob decides to record his goal differential every 4 games.

## The Question

After playing 1 season on Amateur and 1 season on Beginner, on which difficulty level will Bob have a greater goal differential on? How can Bob have a goal differential if he has played 0 games?
FIFA 15 Career Mode Seasons Table

## Identifying the Variables

Independent Variable: Games Played

Dependent Variable: Goal Differential

## Equations for the Table

Let g = games played

Let d = goal differential

d = 2.5g + 3

d= 2g + 17

## The Graph

The points on the x axis represent 4 games played.

For example, 1=4, 2=8 etc.

## Equations of the Lines-Goal Differential Amateur:

y=mx+b

Points: A (1,13) B (8,83)

y2-y1/x2-x1

83-13/8-1

70/7

10=m

y= 10x+b

We can substitute x=1 and y=13 because the line passes through (1,13)

So, 13=10*1+b

13= 10+b

-10+13= b

3 = b

y=10x+3

Standard Form: 10x-y+3=0 or 10x-y= -3

## Equations of the Lines-Goal Differential Beginner:

y=mx+b

Points: A (1,17) B (8,73)

y2-y1/x2-x1

73-17/8-1

56/7

8=m

y= 8x+b

We can substitute x=1 and y= 17 because the line passes through (1,17)

So, 17= 8*1+b

17= 8+b

-8+17=b

9=b

y=8x+9

Standard Form: 8x-y+9=0 or 8x-y= -9

## Point of Intersection/Graphic Solution

Amateur Difficulty Line: y=10x+3

Beginner Difficulty Line: y=8x+9

10x+3=8x+9

-8x+10x=9-3

2x=6

x=6/2

x=3

Substitute 3 in place of x in order to find y value

y=10*3+3

y=33

Therefore, the point of intersection will be (3,33).

This means that at the point (3,33) on the graph, both lines intersect. Therefore, after playing 12 games (remember that each point on the x axis represents 4 games), Bob will have the same goal differential on Amateur and Beginner difficulty levels.

## The Answer to the Questions

At the end of the 2 seasons, Bob will have gotten a greater goal differential while playing on Amateur mode. This is because his goal differential goes up by 10 every 4 games while on Beginner, his goal differential only increases by 8 goals every 4 games.

Bob can have a goal differential while he has played 0 games because Tom starts off each season by playing the first 10 games. Furthermore, Bob is only recording the games he plays so he will not include the first 10 games within his table.