Graphing Direct Variation

An equation of the form y = kx can be thought of as an equation of the form y = mx + b where m = k and b = 0. Thus, a direct variation equation is an equation in slope- intercept form which passes through (0, 0) and has a slope equal to the constant of variation.

Therefore, to graph a direct variation equation, start at (0, 0) and then proceed as you would in graphing a slope. Or, if you know one point, draw a straight line between (0, 0) and that point, and extend the line on both sides.

Example 4: y varies directly as x. If the constant of variation is , graph the line which represents the variation, and write an equation that describes the variation.

y = x

To calculate the constant of variation, given a graph of direct variation, simply calculate the slope.