For the data in the table, does y vary directly with x? If it does, write an equation for direct variation. Show your work. (2 points)
Hint: y = kx is the formula for direct variation. Find k, then substitute it back in to the formula.
25
15
5
10
y
6
2
X
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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.
First, let's find the ratio between two sets of values for y and x.
For the first set of values (25 and 6):
y/x = 25/6 ≈ 4.166
For the second set of values (15 and 2):
y/x = 15/2 = 7.5
For the third set of values (5 and 10):
y/x = 5/10 = 0.5
We can see that the ratio y/x is not the same for all three sets of values. Therefore, y does not vary directly with x.
Since there is no direct variation, we cannot write an equation for direct variation using the formula y = kx.
To determine if y varies directly with x, we can check if the ratio of y to x remains constant.
Let's calculate the ratio for each pair of values:
For the first pair (25, 6):
y1 / x1 = 6 / 25
For the second pair (15, 2):
y2 / x2 = 2 / 15
For the third pair (5, x):
y3 / x3 = y / 5
For the fourth pair (10, x):
y4 / x4 = y / 10
Since the ratio of y to x is not constant, we can conclude that y does not vary directly with x.
Therefore, an equation for direct variation cannot be determined in this case.