Final answer:
Y does not vary directly with x in the equation 3y = -7x - 18 because it includes a y-intercept (-18), which is inconsistent with the definition of direct variation.
Step-by-step explanation:
The student asked whether y varies directly with x and, if so, to find the constant of variation k for the equation 3y = -7x - 18. To determine if y varies directly with x, we compare the given equation to the standard direct variation form y = kx. However, the given equation includes a y-intercept (-18), indicating that y does not vary directly with x because a direct variation should not have a constant term. Instead, it is a linear equation with both a slope and a y-intercept.
In a direct variation situation, the constant of variation is the coefficient of x when the equation is solved for y, but in this case, it's not applicable since the equation does not represent direct variation.