11-15 Class notes Direct Variation

Direct variation describes linear functions whose graphs pass through the origin (0,0).

The constant of variation k in y = kx is the coefficient standing next to the variable, so it is the rate of change in y as x changes.  It is also the slope of the graph.

In our box-stacking example, the height h changes by 10cm each time the number of boxes n increases by 1.  The constant of variation k is 10.  The rate of change is 10cm per box, or 10 cm/box.

Solving for k by isolating k in the equation y = kx (divide both sides by x) gives k = y/x .

If you think of k as a slope, and slope as change in y divided by change in x, that's consistent with k being equal to y divided by x.