Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

Key Concepts

Direct Variation

Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. This can be expressed mathematically as y = kx, where k is the constant of variation. In this case, as x increases or decreases, y changes in direct proportion, maintaining the ratio k.

Finding the Constant of Variation

To find the constant of variation (k) in a direct variation problem, you can use known values of x and y. By rearranging the direct variation formula to k = y/x, you can substitute the given values. For example, if y = 20 when x = 4, then k = 20/4 = 5, establishing the relationship between x and y.

Substituting Values

Once the constant of variation is determined, you can find the value of y for any given x by substituting x into the direct variation equation. For instance, if k = 5, to find y when x = -6, you would calculate y = 5 * (-6), resulting in y = -30. This process allows you to explore the relationship between the variables across different values.