how can direct variation be easily identified on a table equation on a graph?
To easily identify direct variation on a table, equation, or graph, you need to look for a consistent relationship between two variables. Direct variation, also known as direct proportion, occurs when one variable increases or decreases in proportion to the other variable.
Here's how you can identify direct variation using different representations:
1. Table: In a table, look for a constant ratio between corresponding values of the two variables. If you divide the values of one variable by the values of the other variable, and the resulting quotient is always the same, then you have direct variation.
For example, consider the table below:
| x | y |
--------------
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
In this table, if you divide the values of y by the corresponding x-values, you will always get 2. This shows a constant ratio, indicating direct variation.
2. Equation: In an equation, direct variation is represented by the form y = kx, where k is a constant. The constant k represents the ratio between the variables. If the equation can be simplified to this form, then it represents direct variation.
For example, the equation y = 3x represents direct variation because it can be written in the form y = kx, where k = 3.
3. Graph: On a graph, direct variation is represented by a straight line passing through the origin (0,0). If all the points on the graph lie on a straight line passing through the origin, it indicates direct variation.
For example, consider a graph where all the points fall on a straight line passing through the origin. This indicates direct variation.
By looking for these patterns and relationships, you can easily identify direct variation in a table, equation, or graph.