How do you find direct variation when given X and Y?
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How do you find direct variation when given X and Y?
Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
What is the equation when y 12 x 2?
Explanation: As x and y are inversely proportional, the equation can be represented as x=ky . Substituting x=2 and y=12 , we get 2=k12 => k=12⋅2 => k=24 .
What does it mean when it says y varies directly with x?
This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same. The graph of the direct variation equation is a straight line through the origin. Example 1: Given that y varies directly as x , with a constant of variation k=13 , find y when x=12 .
What are X and Y called in the equation x/y 12?
The variable x is called the independent variable (also sometimes called the argument of the function), and the variable y is called dependent variable (also sometimes called the image of the function.) For y=12, there are two possible x’s. x=-4, and x=4.
How do you solve joint variations?
Joint Variation
- If more than two variables are related directly or one variable changes with the change product of two or more variables it is called as joint variation.
- If X is in joint variation with Y and Z, it can be symbolically written as X α YZ.
- Equation for a joint variation is X = KYZ where K is constant.
What is the equation relating X and Y together?
y = kx
a. Because x and y vary directly, the equation is in the form y = kx.
How do you say that Y varies directly with X?
We say y varies directly with x (or as x , in some textbooks) if: for some constant k , called the constant of variation or constant of proportionality . (Some textbooks describe direct variation by saying ” y varies directly as x “, ” y varies proportionally as x “, or ” y is directly proportional to x .”)
Which equation describes the direct variation of X?
For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x. Example 1: If y varies directly as x, and x = 12 when y = 9, what is the equation that describes this direct variation? k = = y = x.
What is the constant of variation when x = 2?
For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
What is a direct variation relationship?
We will focus here on a linear relationship between two variables where one is a constant multiple of the other. This is a special relationship called direct variation. In general, we say that y varies directly as x if there is a constant k so that the equation is true.