T.i.P.S.

Students should determine the differences between proportional and nonproportional situations or relationships. Students should know that linear relationships can be represented as words, tables, graphs, and equations. Nonproportional relationships will affect these representations because the yintercept in the graph will no longer be zero, the ratios in the table will not be proportional, and the equation will be affected because the number will be added or subtracted which is represented by b. Students should know that two variables show direct variation if y = kx and k is not equal to zero. k represents the constant of proportionality. In the equation, the two variables, y and x, vary directly to each other as they represent proportional relationships.
Example

Which of the following represents a proportional relationship? Justify your thinking.
a) I and II
b) I and IV
c) III and IV
d) II and III
Hint
Possible Solution
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TEKS

8.5 Proportionality. The student applies mathematical process standards to use proportional and nonproportional relationships to develop foundational concepts of functions. The student is expected to:
(F) distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0