Question

What relationship is described by the formula below? (mass of the element/mass of the compound) x 100

Answer 1

Introduction
empirical formula
A table of values shows a list of the values for an independent variable, x, matched with the value of the dependent variable, y. In many cases, an equation can be used to relate the two values. If you know the equation, you can easily generate a table of values.


If you are given the table of values, you must determine how the two values are related and then write an equation that shows the relationship.

xy-2-1-100112When looking at the relationship between the y-values and the x-values, it's easy to see that each y-value is 1 more than the x-value. Therefore, the equation that describes this relationship is y = x + 1.

 

Develop a Rule When Given a Table of Values

Writing an Equation for a Table of Values

Look at the table below. There does not appear to be a constant rate of change.



In this example, we look at the ratio of the change in the pattern of y-values and x-values.









Even though there did not appear to be a constant rate of change, there is actually a constant rate of change of 2.

We're almost ready to write our equation.

We now know the value for m (the slope) in the equation y = mx + b is 2. Since m is 2, we know that each x-value is being multiplied by 2.

What else is happening to the x-value to get the corresponding y-value?

xProcessy-32(-3) + 3-3-12(-1) + 3132(3) + 3962(6) + 31572(7) + 317

We also need to add 3 to the product in order to get the corresponding y-value.

The equation that represents this table of data is y = 2x + 3.