Direct Variation

Direct Variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as $$y = kx$$ , where $$k$$ is a non-zero constant.

The Direct Variation Equation is $$y = kx$$ , where $$y$$ varies directly with $$x$$ and $$k$$ is the constant of variation.

The constant of variation, denoted as $$k$$ , represents the ratio of the two variables in a direct variation relationship.

A direct variation always passes through the origin, represented by the ordered pair (0, 0).

To find $$k$$ , use the formula $$k = \frac{y}{x}$$ , where $$y$$ is the value of the dependent variable and $$x$$ is the value of the independent variable.

Using the formula $$k = \frac{y}{x}$$ , we find $$k = \frac{14}{6} = \frac{7}{3}$$ .

A direct variation relationship can be expressed as $$y = kx$$ , where $$k$$ is the constant of variation.

If $$x$$ is doubled, $$y$$ will also double, since they are directly proportional.

An example of direct variation is the relationship between distance and time when traveling at a constant speed. If speed is constant, distance varies directly with time.

First, find $$k = \frac{y}{x} = \frac{5}{2}$$ . The equation is $$y = \frac{5}{2}x$$ .