Final answer:
The student's error is not understanding that in direct variation, the constant ratio of y to x must be maintained. Given that y = 9 when x = -3, the constant of variation is -3, which means y should be -6 when x = 2, not -4.
Step-by-step explanation:
The error made by the student in saying that if y varies directly with x and y = 9 when x = -3, then y = -4 when x = 2, is a misunderstanding of the concept of direct variation. In direct variation, the ratio of y to x is constant. This means that if we find the constant of variation (k) when y is 9 and x is -3, we must use the same k to find y when x is 2.
To find the constant of variation, we use the equation y = kx, which gives:
9 = k(-3)
k = -3
Now using this k to find y when x is 2, we get:
y = kx
y = -3(2)
y = -6
Therefore, if y varies directly with x and y = 9 when x = -3, then y should be -6 when x = 2, not -4 as the student incorrectly suggested.