Question

George observes that for every increase of 1 in the value of x, there is a increase of 60 in the corresponding value of y. He claims that the relationship represented by the table is proportional. critique George's reasoning.
Table for x: 1, 2, 3, 4, 5
Table for y: 90, 150, 210, 270, 330

Answer 1

Hi there!

FACTS :

To see if multiple ratios are proportional, you can write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportionnal ratios. You can also write them as fractions and divide the numerator (top number) by its denominator (bottom number), and compare the decimal numbers the same way you would compare the fractions (I personnaly find this method easier because you don't need to simplify the fractions).

STEPS TO ANSWER:

x = 1 ; y = 90 → $\frac{1}{90} =$ 1 ÷ 90 = 0.01111111...

x = 2 ; y = 150 → $\frac{2}{150} =$ 2 ÷ 150 = 0.0133333...

x = 3 ; y = 210 → $\frac{3}{210} =$ 3 ÷ 210 = 0.01428571

x = 4 ; y = 270 → $\frac{4}{270} =$ 4 ÷ 270 = 0.0148148...

x = 5 ; y = 330 → $\frac{5}{330} =$ 5 ÷ 330 = 0.01515152

** You didn't really need to calculate them all because even the first two decimal numbers weren't equivalent, but I wanted to show you the whole process so I calculated them all.

⇒ If you compare all the decimals you got, you can easily see that they are not the same, which means that the ratios between the values of "x" and the values of "y" are not proportional. Therefore, George's reasoning wasn't good.

There you go! I really hope this helped, if there's anything just let me know! :)