Answer:
The values in the table suggest that there is a mathematical relationship between the two variables X and Y. Upon inspection, we can observe that Y is increasing with respect to X, and the increase seems to be non-linear. Specifically, as X increases by a factor of 2, Y increases by a factor of approximately 1.5 to 2.
Based on these observations, it seems that the relationship between X and Y may be an exponential one. To confirm this, we can plot the data points on a graph and see if they form a curve that resembles an exponential function.
Alternatively, we can calculate the ratio of Y to X and see if it remains approximately constant. This can be done by dividing each value of Y by its corresponding value of X:
1/5 = 0.2
2/10 = 0.2
3/15 = 0.2
5/25 = 0.2
8/40 = 0.2
The ratio remains constant at approximately 0.2, suggesting that the relationship between X and Y may be a proportional one, with a constant of proportionality equal to 0.2.
Therefore, the table represents a proportional relationship between X and Y, where Y is proportional to X with a constant of proportionality equal to 0.2.
Explanation:
Here's a step-by-step explanation of how to evaluate the table:
1. Identify the variables: The table contains two variables, X and Y, which are listed in two separate columns.
2. Examine the values: Look at the values in the table for both X and Y. Notice that as X increases, so does Y.
3. Determine the pattern: To determine the pattern between the two variables, calculate the ratio of Y to X. If the ratio is constant, then the relationship is proportional. If the ratio changes, then the relationship is nonlinear.
4. Calculate the ratio: To calculate the ratio, divide each value of Y by its corresponding value of X. For example, to find the ratio for the first row, divide 1 by 5: 1/5 = 0.2. Continue calculating the ratios for each row.
5. Analyze the ratio: If the ratios are approximately constant, then the relationship is proportional. In this case, we see that the ratios are all approximately 0.2, so we can conclude that the relationship is proportional.
6. Determine the constant of proportionality: To determine the constant of proportionality, simply use any one of the rows in the table. For example, let's use the first row, where X = 5 and Y = 1. The ratio of Y to X is 0.2, so we can write the relationship as Y = 0.2X. This means that for every increase of 1 unit in X, Y increases by 0.2 units.
7. Summarize the result: Based on the analysis, we can say that the table represents a proportional relationship between X and Y, with a constant of proportionality equal to 0.2.