Question

Write an equation for a direct variation that includes the point (3, 18)

Answer 1

Direct variation means that the line goes through the origin of the graph, so you know that the line must go through point (0,0). Using that along with the given point, you can find the slope of the line.

m = $\frac{y_2 - y_1}{x_2 - x_1}$
m = $\frac{18 - 0}{3 - 0}$
m = $\frac{18}{3}$
m = 6

Now that you know the slope of the line you are looking for is 6, you can plug that into a point-slope form equation and find the equation of your line.

y - y_1 = m (x - x_1)   Plug in either set of coordinate. I chose (3, 18).
  y - 18 = 6 (x - 3)        Use he Distributive Property
  y - 18 = 6x - 18         Add 18 to both sides
        y = 6x

The equation of a direct variation line that includes the point (3, 18) is y = 6x.