TOWN POPULATIONS

By: Vidhi Trivedi

Situation

The difference in growth of a big town compared to a small town population over the course of 11 years.

Classification of variables

· t = total population

· p = people

Data (table):

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Equations in forms of y=mx+b and Ax+By=C

y = mx + b form:

Big Town population equation: t = -500p + 10,025

Small Town population equation: t = 300p + 600

Ax + By = C form:

Big Town population equation: 500p + t = 10, 025

Small Town population equation: 300p + t = 600

Graph and POI

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Graphic Solution

-500x + 10,025 = 300x + 600

-500x - 300x = 600 - 10, 025

-800x = -9425

-800/-800 = =9425/-800

x = 11.78

Substitute x= 11.78 in y= -500x + 10,025

y= -500 (11.78) + 10,025

y= -5890 + 10,025

y= 4135


Therefore, POI = (11.78, 4135)

Explanation of significance

Particularly, the intersection marks where the two lines meet. Since this point is on both lines, (in the graph show above) it solves both the equations. Hence, we can say that the point of intersection solves the entire system of equation.

Summary Statement

The population of the big town decreases throughout eleven years and the population of the small town increases throughout eleven years. Also, at point (11.78, 4135), they had the same population.

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