how can direct variation be easily identified on a table equation on a graph?
The y values must be a constant times the x values.
So, check any pair, and make sure the other pairs are related by the same multiple.
On a graph, it will be a straight line passing through (0,0)
To easily identify direct variation on a table, equation, or graph, you need to look for a specific pattern. Direct variation, also known as direct proportionality, occurs when two variables change in such a way that their ratio remains constant.
1. On a table:
- Look at the values of the two variables.
- If you divide each value of one variable by the corresponding value of the other variable, and the ratios are always the same, then it is a direct variation.
- For example, if the second column is triple the first column for each row, it indicates direct variation.
2. In an equation:
- The equation representing direct variation has the form y = kx, where k is a constant.
- The constant k represents the ratio between the two variables and remains the same throughout.
- If the equation fits this form, then it represents direct variation.
3. On a graph:
- If the points on a graph lie on a straight line passing through the origin (0,0), it indicates direct variation.
- The slope of this line is equal to the constant k in the equation.
- So, if a graph shows a linear relationship starting from the origin, it is a direct variation.
Remember, in direct variation, as one variable increases, the other variable also increases, but their ratio remains constant. Conversely, as one variable decreases, the other variable also decreases.
By observing the patterns and applying these methods, you can easily identify direct variation on a table, equation, or graph.