The ordered pairs (2a, 3a) represent all the ratios equivalent to 2:3 from a multiplicative perspective.
What to look forInterpreting the patterns in the ratio table and in the graph of equivalent ratios introduces students to the notion of rate of change—or slope and slope triangles—as well as to similar triangles. Note that the number 0 cannot be used in a ratio. For example, 0:0 does not make sense because equivalent ratios are generated by multiplying or dividing each value in a ratio by the same positive number.
Which of the following points will lie on the line that contains points associated with the collection of ratios equivalent to 8:5?
a. (10, 16) b. (2, 1.25) c. (24, 15) d. (14, 11)
Answer: b) (2, 1.25) and c) (24, 15)