Question

Use the table to answer these questions. a. What does x represent? b. What does y represent?c. Is there a proportional relationship between x and y?

Answer 1

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.

Step-by-step 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,

`\begin{gathered} x=k* y \\ x=ky \\ \text{Therefore,} \\ (x)/(y)=k \\ \text{When x=1 and y=}(1)/(4),\text{ then} \\ k=(x)/(y) \\ k=1\text{ / }(1)/(4) \\ k=1*(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=}(x)/(y) \\ \text{When k=}(x)/(y) \\ \text{Then y=}(x)/(k) \end{gathered}`

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.