Final answer:
The direct variation equation where y varies directly as x, with the given condition y=8 when x=14, is y = (4/7)x.
Step-by-step explanation:
The student is asking for a direct variation equation where y varies directly as x. When y varies directly with x, the relationship between them can be represented by the equation y = kx, where k is the constant of variation. To determine the value of this constant, we use the given condition that when x = 14, y = 8. Substituting these values into the equation gives us 8 = k(14). To find k, we divide both sides of the equation by 14, which gives us k = 8/14 or k = 4/7. Therefore, the final direct variation equation is y = (4/7)x.