To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for each pair of values.
Ratio of y to x for the first pair of values:
y = 7.5, x = -3
Ratio = y / x = 7.5 / -3 = -2.5
Ratio of y to x for the second pair of values:
y = 2.5, x = -1
Ratio = y / x = 2.5 / -1 = -2.5
The ratio of y to x is the same for both pairs of values, -2.5. This means that y varies directly with x.
To write the equation for direct variation, we can use the form y = kx, where k is the constant of variation.
Using the values from any pair of values (let's use the first one with x = -3 and y = 7.5):
7.5 = k * -3
Divide by -3:
7.5 / -3 = k
-2.5 = k
Therefore, the equation for direct variation is y = -2.5x.
tell whether y varies directly with x. if it does, write and equation for the direct variation.
x= -3, -1, 2, 5
y= 7.5, 2.5, -5, -12.5
1 answer