TOWN POPULATIONS
By: Vidhi Trivedi
Situation
Classification of variables
· t = total population
· p = people
Data (table):
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
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.