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

1. 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.
2. If X is in joint variation with Y and Z, it can be symbolically written as X α YZ.
3. 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.