Question

A direct variation function contains the points (2,14) and (4,38) which equation represents the function

Answer 1

You are given two points on a line, and told that the function is "direct variation."  You can save a lot of time by recognizing that the y-intercept here is zero (0).  Thus, the line passes through the origin.

A line through (2,14) and (4,38) is NOT direct variation, because the line connecting those two points does NOT pass through the origin, and thus has a vertical intercept.