Students should determine the differences between proportional and non-proportional situations or relationships. Students should know that linear relationships can be represented as words, tables, graphs, and equations. Non-proportional relationships will affect these representations because the y-intercept 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.
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
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8.5 Proportionality. The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to:
(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