Determine whether y varies directly with x. If so, find the constant of variation and write the equation.
X | Y
------
1 | -2
3 | -6
5 | -10
i think it's A ??
A. yes; k=2 and y=2x
B. no
C. yes; k= -2 and y= -2x
D. yes; k= -1/2 and y= -1/2x
C is correct
or is it C ???
A
C
C
B
C
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To determine whether y varies directly with x, we need to check if the ratio between y and x remains constant for all corresponding values. We can do this by calculating the ratio of y to x for each given pair of values.
So, let's calculate the ratio of y to x for the given pairs:
For the first pair (1, -2):
y / x = -2 / 1 = -2
For the second pair (3, -6):
y / x = -6 / 3 = -2
For the third pair (5, -10):
y / x = -10 / 5 = -2
Since the ratio y/x is the same (-2) for all the pairs, we can conclude that y varies directly with x.
Now, let's find the constant of variation, represented by the letter k. The constant of variation is the value that relates y to x in the equation y = kx.
We can find k by choosing any pair of values and substituting them into the equation. Let's use the first pair (1, -2):
-2 = k * 1
Solving for k, we get k = -2.
Therefore, the equation that represents the direct variation relationship between y and x is y = -2x.
So, the correct answer is:
C. yes; k = -2 and y = -2x