Is #3x+y=6# a direct variation and if it is, how do you find the constant?
y = -3x + 6
It is direct variation, and the constant is: -3.
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The equation (3x + y = 6) represents a direct variation if it can be written in the form (y = kx), where (k) is the constant of variation. To determine if it is a direct variation and to find the constant, we need to solve the equation for (y).
Starting with: [3x + y = 6]
Subtract (3x) from both sides to isolate (y): [y = -3x + 6]
The equation is now in the form (y = mx + b), where (m = -3) and (b = 6). Since there is a y-intercept ((b ≠ 0)), this equation does not represent a pure direct variation because a direct variation passes through the origin (0,0) and has no y-intercept other than 0. Therefore, (3x + y = 6) is not a direct variation, and there is no constant of variation in the form (y = kx) for this equation.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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