tell whether x and y show direct variation and explain reasoning
x and y show no variation here. Cannot copy and paste on these posts.
To determine if two variables, let's say x and y, show direct variation, you need to check if the ratio between them remains constant. In other words, if y is directly proportional to x, multiplying x by a certain constant value will result in y being multiplied by the same constant value.
To explain this reasoning, you can follow these steps:
1. Gather a set of data points: Collect a set of values for both x and y. Make sure you have multiple data points to observe any patterns.
2. Calculate the ratio: For each pair of data points, divide the value of y by the corresponding value of x. This will give you a set of ratios.
3. Check for consistency: Now, examine the ratios you obtained from step 2. If the ratios remain constant for all pairs of x and y, then it indicates direct variation. If the ratios vary significantly, there is likely no direct variation.
For example, let's say we have the following data points:
x: 2, 4, 6, 8
y: 3, 6, 9, 12
The ratios for each pair of x and y are as follows:
2/3 = 0.67
4/6 = 0.67
6/9 = 0.67
8/12 = 0.67
In this case, the ratios remain constant at approximately 0.67 for all data pairs. This indicates that x and y show direct variation.
Remember, direct variation means that multiplying one variable by a constant value results in the other variable being multiplied by the same constant value.