1. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
x
y
10
15
16
24
20
30
(1 point)
yes; y = 1.5x
yes; y = 2x
yes; y = x + 5
y does not vary directly with x
Your table is confusing.
However, it appears that the answer is
yes; y = 1.5x
ok thx so much ms.sue i thought i had answered that right
You're very welcome, Freddy. :-)
To determine if y varies directly with x, we can check if the ratio between y and x remains constant for all values in the table.
Let's calculate the ratios:
For x = 10, y = 15, the ratio is 15/10 = 1.5.
For x = 16, y = 24, the ratio is 24/16 = 1.5.
For x = 20, y = 30, the ratio is 30/20 = 1.5.
As we can see, the ratio between y and x is 1.5 for every pair of values. This indicates that y varies directly with x.
Now, let's write an equation to represent this direct variation.
The equation for direct variation is of the form y = kx, where k is the constant of variation. We can determine the value of k by using any of the data points. Let's use the first data point (x = 10, y = 15):
15 = k * 10
Dividing both sides by 10, we get:
k = 15/10
Simplifying, k = 1.5.
Therefore, the equation for the direct variation is y = 1.5x.
So the correct answer is: yes; y = 1.5x.