Question

How do you tell if a graph shows direct variation?

Answer 1

A graph shows direct variation if it goes through the origin, `(0,0)`. The equation is `y=kx`, where `k` is a constant, which is apparent when we write the equation as `y/x=k`. In slope-intercept form, the equation would be `y=mx+b`, where `m=k`, and `b=0`.

Lets suppose that `k=m=2`. The slope-intercept form would be `y=2x+0`. The following is the graph for this equation.
graph{y=2x+0 [-10, 10, -5, 5]}