Direct Variation Rate of Change

In the formula, y=kx, k is referred to as the constant of variation OR the constant of proportionality. It is the coefficient of x (not y!)

A constant does not change in value.

Step 1. Plot a point on the origin, (0,0).

Step 2. Use k like you would slope to plot two more points.

Step 3. Connect the points with a line (with arrows on each end!)

1. Using y = kx and solve for k by dividing both sides by x:   $\frac{y}{x}$  =k
2. Substitute in the x and y-values of the point on the direct variation to determine the constant of variation:    $\frac{2}{-1}$  =k or k = -2

This video is less than two minutes in length and shows one way of solving "varies directly with x" problems. ("directly proportional problems are done the same way)

Remember that y = kx is the same as y = ax.

For each ordered pair given, (-4,1),(-3,0.75). (-2. 0.5) and (-1,0.25) if you divide the y value by the x value you find k for the ordered pairs. IF k is the same for each, then you have a direct variation and have found the constant of variation/the constant of proportionality