Do the data points (2,9), (-4,8), and (7,3) show a direct variation?
Given the data points (2, 9), (-4, 8), and (7, 3), the relationship shows a direct variation. is that true or false?
Given the data points (2, 9), (-4, 8), and (7, 3), the relationship shows a direct variation.
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To determine if the data points (2,9), (-4,8), and (7,3) show a direct variation, we need to check if the ratio of the corresponding y-values to x-values is constant for all the data points.
Let's calculate the ratios for each pair of points:
For the first pair (2,9):
Ratio = 9/2 = 4.5
For the second pair (-4,8):
Ratio = 8/-4 = -2
For the third pair (7,3):
Ratio = 3/7 ≈ 0.43
Since the ratios are not constant for all the data points, we can conclude that the data points do not show a direct variation.
However, it's important to note that direct variation can only be determined by two data points. In this case, we have three, which may not fit a direct variation relationship, but we can still observe the relationship between the data points.