For this problem, tell whether each relationship is a direct variation. Explain.
x | -3 | -6 | -9 |
y | 18 | 36 | 54 |
My teacher didn't really explain direct variation very well, but i did catch that you put x over y. (Hopefully this helps)
To determine whether a relationship is a direct variation, you need to check if there is a constant ratio between the two variables being compared. In this case, it means dividing the x-values by the corresponding y-values to see if the ratio is the same for all values.
Let's calculate the ratios for the given values of x and y:
For the first pair of values: x = -3, y = 18
-3 divided by 18 = -1/6
For the second pair of values: x = -6, y = 36
-6 divided by 36 = -1/6
For the third pair of values: x = -9, y = 54
-9 divided by 54 = -1/6
Since the ratio of x to y is the same (-1/6) for all the given values, we can conclude that the relationship between x and y is a direct variation.
In general, a direct variation is represented by the equation y = kx, where k is the constant ratio between x and y. In this case, the constant ratio is -1/6.