Question

For each table determine whether it shows x and y are proportional

Answer 1

To obtain the relationship between x and y, the following steps are advised:

Step 1: Starting with the values in table 1, divide the values of y by the corresponding values of x, as follows:

`\begin{gathered} when\text{ x=}6,\text{ y=24, } \\ \Rightarrow\text{thus: }(y)/(x)=(24)/(6)=4 \\ when\text{ x=8},\text{ y=40, } \\ \Rightarrow\text{thus: }(y)/(x)=(40)/(8)=5 \\ when\text{ x=10},\text{ y=60, } \\ \Rightarrow\text{thus: }(y)/(x)=(60)/(10)=6 \end{gathered}`

Since the value of the ratio of y to x is not constant (ranging from 4, to 5, and to 6), it means that x and y are NOT proportional.

Therefore, for Table 1, x and y are NOT proportional

Step 2: Proceeding with the values in table 2, divide the values of y by the corresponding values of x, as follows:

`\begin{gathered} when\text{ x=}6,\text{ y=18, } \\ \Rightarrow\text{thus: }(y)/(x)=(18)/(6)=3 \\ when\text{ x=9},\text{ y=27, } \\ \Rightarrow\text{thus: }(y)/(x)=(27)/(9)=3 \\ when\text{ x=12},\text{ y=36, } \\ \Rightarrow\text{thus: }(y)/(x)=(36)/(12)=3 \end{gathered}`

Since the value of the ratio of y to x is constant ( 3, all through), it means that x and y are proportional.

Therefore, for Table 2, x and y are proportional

Thus: y is 3 times x, for table 2