tell whether the relationship is a direct variation. explain answer..
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x -3 -6 -9
y 18 36 54
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it looks like the x is multiplied by 6 to get y
so what do you think?
To determine if the relationship is a direct variation, we need to check if the ratio of y to x remains constant.
In this case, we can calculate the ratio of y to x for each pair of values:
For the first pair (-3, 18): y/x = 18/-3 = -6
For the second pair (-6, 36): y/x = 36/-6 = -6
For the third pair (-9, 54): y/x = 54/-9 = -6
Since the ratio of y to x remains the same (-6) for all the pairs, we can conclude that the relationship is a direct variation.
In a direct variation, the ratio of the two variables is always constant. In this example, as x decreases by a factor of 3 (-3 to -6 to -9), y also decreases by the same factor of 3 (18 to 36 to 54). Therefore, the relationship between x and y is a direct variation.