In the table shown,
(a) the x values represents the INDEPENDENT VARIABLE
(b) the y values represents the DEPENDENT VARIABLES
This simply means, every value of y will depend on the value of x.
(c) There is a proportional relationship between x and y.
Explanation:
For every value given for x, there is a corresponding value for y. This means there is a constant rate between every pair of x and y values. This constant rate is mathematically expressed as k. That is,
[tex]\begin{gathered} x=k\times y \\ x=ky \\ \text{Therefore,} \\ \frac{x}{y}=k \\ \text{When x=1 and y=}\frac{1}{4},\text{ then} \\ k=\frac{x}{y} \\ k=1\text{ / }\frac{1}{4} \\ k=1\times\frac{4}{1} \\ k=4 \\ \text{Having calculated k = 4, then everytime you have a value for x} \\ y\text{ can be derived from the formula k=}\frac{x}{y} \\ \text{When k=}\frac{x}{y} \\ \text{Then y=}\frac{x}{k} \end{gathered}[/tex]
The above explanation shows that the value of x and the corresponding value of y would follow the same pattern, no matter the value given to x at any point. Therefore there is a proportional relationship between x and y.
