The All-Stars vs. The Math Maniacs

BY: AHALYA IYNKARAN (Period 2)

The All stars vs. Math Maniacs

Two teams from Ontario, the All-Stars and the Math Maniacs compete in a nation wide basketball tournament held at Toronto. Their rankings are shown below. Which team should Tyler root for?

The All-Stars

As the y-intercept indicates, the All-Stars start off the game with a rank of 18 (0,18). During the game the All-stars progress with -2 ranks per game. By their last game, they finish off at rank 8. This data can also be represented in equation form such as, r = -2n+18 (y-intercept form) or 2n+r-18 = 0 (standard form).


N = Number of games (independant variable).

R = Rank (dependant variable).

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The Math Maniacs

Even though the Math Maniacs start off at rank 30 (0,30), they progress at a rate of -5 per game. They beat the All-Stars by finishing off at a high rank 5. This data can also be represented by slope y-intercept form, r = -5n+30 or in standard form, 5n+r-30 = 0.


N = Number of games (independant variable).

R = Rank (dependant variable).

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At what point did both teams intersect?

The rankings of both teams, the All-Stars and the Math Maniacs are graphed above. It is clear that the point of intersection, where the two teams are tied at the same rank at the number of game is (4,10). This simply means that both teams were tied at rank 10 during their 4th game.
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Significance

If Tyler is only going to the first 3 games, he should root for the All-stars because before the point of interception the All-stars have a better ranking compared to the Math Maniacs. Although if he's attending the match after the 4th game the best team to root for is the Math Maniacs providing that after the point of interception, the rankings for the Math Maniacs are better. However if Tyler is only planning to attend the 4th game, it does not matter which team he cheers for because acccording to the point of intersection, both teams will be tied at rank 10 on their 4th game. So the team Tyler should cheer for depends on which game(s) he will be attending.

In conclusion, the All-stars and the Math Maniacs will both be tied at rank 10 by their 4th game.