Question

Mandy used the input and output in this table to write ratios. She concluded that because that they are not all equivalent, this is not a proportional relation ship. Is she correct. Explain.I dont get what she means by, "because they are not all equivalent"

Answer 1

The problem is stating that Mandy found the ratio between input and output of many points on the graph, which are displayed by the fractions. Mandy's conclusion was that they were not equivalent, meaning they were different and that is why the function is not proportional. Mandy's conclusion is wrong, the relation is proportional. If we take all the functions we have:

$\frac{5}{1}=\frac{10}{2}=\frac{25}{5}=\frac{50}{10}$

Where the input is the denominator and the output is the numerator we will have a ratio of "5". Mandy's mistake was to invert the last fraction, she inserted the output in the denominator, this is why she said the were different.