does y vary directly with x? if it does, write an equation for the direct variation.
x = 10, 16, 20
y= 15, 24, 30
I need help pls I don't understand.
well, for the 20 and 30
y = (3/2) x = 1.5 x
does that work for
24 = 1.5 * 16 ?
and for
15 = 1.5 * 10 ?
if so then y = 1.5 x, a direct variation, is it.
To determine if y varies directly with x, we need to check if there is a constant ratio between the values of y and x. In other words, if y increases or decreases at the same rate as x.
Let's calculate the ratios of y to x for each set of values given:
For the first set of values:
y/x = 15/10 = 1.5
For the second set of values:
y/x = 24/16 = 1.5
For the third set of values:
y/x = 30/20 = 1.5
Since the ratios are all equal to 1.5, we can conclude that y varies directly with x.
To write an equation for direct variation, we can use the form: y = kx, where k is the constant of variation.
To find the value of k, we can use any of the given points (x, y). Let's choose the first set of values (x = 10, y = 15):
15 = k * 10
Now, solve for k:
k = 15/10 = 1.5
Therefore, the equation for direct variation is:
y = 1.5x