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)
(-10,25)
(1,-2.5)
(6,-15)
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all values.
For the given data, we can calculate the ratio of y to x for each pair:
(-10, 25): 25 / -10 = -2.5
(1, -2.5): -2.5 / 1 = -2.5
(6, -15): -15 / 6 = -2.5
The ratio of y to x is -2.5 for all data pairs, which means y varies directly with x.
To write the equation for the direct variation, we can use the formula y = kx, where k is the constant of variation. Since the ratio is -2.5 for all pairs, we can set k = -2.5:
Therefore, the equation for the direct variation is y = -2.5x.