8.5.E 8.5.F 8.5.H

Texas Essential Knowledge and Skills (TEKS) Proportional vs. Not Proportional
Grade:	8th Grade
Standard:	8.5.E
Description:	solve problems involving direct variation;
Standard:	8.5.F
Description:	distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0;
Standard:	8.5.H
Description:	identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and

The relationship between two variables, say x and y, is proportional
if there exists a constant, say k, such that y equals kx.

In a proportional relationship, the constant is
often referred to as the constant of proportionality.

Consider the known relationship between inches and feet. There are 12 inches in 1 foot.
If we want to know the number of inches, y, in a given number of feet, x, we can use the equation y = 12x.
This equation represents a proportional relationship, and 12 is the constant of proportionality.
In some situations, this constant is referred to as the unit rate.
In this situation, the unit rate can be interpreted as 12 inches per foot.

Sometimes values are presented in a table.
How can we determine if a table represents a proportional relationship?
We have to determine if there exists a constant such that each output value is the product of the constant and the corresponding input value.

Texas Essential Knowledge and Skills (TEKS)

Proportional vs. Not Proportional

8.5.E

solve problems involving direct variation;

8.5.F

distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0;

8.5.H

identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and