For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
X
Y
4.5
3
7.5
5
10.5
7
Does y vary directly with x?
If yes, write an equation for the direct variation:
To check if y varies directly with x, we need to compare the ratios of y to x for all the data points.
First, let's find the ratio for the first data point (4.5, 3):
3/4.5 = 0.67
Now, let's find the ratio for the second data point (7.5, 5):
5/7.5 = 0.67
Finally, let's find the ratio for the third data point (10.5, 7):
7/10.5 = 0.67
As we can see, the ratios for all the data points are the same, which means that y varies directly with x.
Now, let's find the equation for the direct variation. The equation for direct variation is in the form y = kx, where k is the constant of variation. To find k, we can choose any pair of x and y values and substitute them into the equation. Let's choose the first data point (4.5, 3):
3 = k * 4.5
To solve for k, divide both sides of the equation by 4.5:
3/4.5 = k
Simplifying, we get:
k = 0.67
Therefore, the equation for the direct variation is:
y = 0.67x