Final answer:
The equation y - 5x = 0 represents a linear equation, which means that y varies directly with x. The constant of variation in this equation is -5.
Step-by-step explanation:
To determine if y varies directly with x, we need to check if the equation y - 5x = 0 represents a linear equation. If it does, then y varies directly with x. In this case, the equation is linear because it is in the form y = mx + b, where m is the slope and b is the y-intercept.
The slope of the equation is -5, which means that for every change in x by 1 unit, y changes by -5 units. Since the equation is linear and y changes by a constant factor of -5, we can conclude that y varies directly with x.
The constant of variation (k) is the coefficient of x in the equation, which in this case is -5. Therefore, the constant of variation for this equation is -5.