For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
(x,y)
(-15,27)
(1,-1.8)
(10,-18)
To determine if y varies directly with x, we need to check if the ratios of y to x are always the same. Let's calculate the ratios for each pair (x,y):
For (-15,27), the ratio is 27 / -15 = -1.8.
For (1,-1.8), the ratio is -1.8 / 1 = -1.8.
For (10,-18), the ratio is -18 / 10 = -1.8.
Since the ratios are always the same (specifically, -1.8), we can conclude that y varies directly with x.
The equation for direct variation is given by y = kx, where k is the constant of variation. We can find k by using any of the pairs, e.g. (-15,27):
27 = k * (-15)
27 / -15 = k
k = -1.8
Therefore, the equation for direct variation is y = -1.8x.