How do I write an equation of direct variation using two given coordinate points?

Question

I have two questions on my algebra homework that relate to direct variation and I can't remember how to use it.

Answer 1

If y varies directly as x, then y = kx, for some constant, k.  Usually in this type of problem, you are given both coordinates of a point and only one coordinate of the other point.  Use the first point to find k.  Then, plug in the known coordinate of the second point and solve for the other coordinate.

 

Example:  y varies directly as x.  If y = 12 when x = 2, then find y                       when x = 20.  

 

  Solution:  y = kx

                Since y = 12 when x = 2, 12 = 2k.  So, k = 6

 

                Therefore, y = 6x

 

                So, when x = 20, y = 6(20) = 120