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:
[tex]\begin{gathered} when\text{ x=}6,\text{ y=24, } \\ \Rightarrow\text{thus: }\frac{y}{x}=\frac{24}{6}=4 \\ when\text{ x=8},\text{ y=40, } \\ \Rightarrow\text{thus: }\frac{y}{x}=\frac{40}{8}=5 \\ when\text{ x=10},\text{ y=60, } \\ \Rightarrow\text{thus: }\frac{y}{x}=\frac{60}{10}=6 \end{gathered}[/tex]
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:
[tex]\begin{gathered} when\text{ x=}6,\text{ y=18, } \\ \Rightarrow\text{thus: }\frac{y}{x}=\frac{18}{6}=3 \\ when\text{ x=9},\text{ y=27, } \\ \Rightarrow\text{thus: }\frac{y}{x}=\frac{27}{9}=3 \\ when\text{ x=12},\text{ y=36, } \\ \Rightarrow\text{thus: }\frac{y}{x}=\frac{36}{12}=3 \end{gathered}[/tex]
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
