Final answer:
The student's question involves identifying the equation of the form y = kx, which represents a direct variation. The provided options a) y = 1/3x, b) y = 2/3x, c) y = 3x, and d) y = 4x are all valid forms of this equation.
Step-by-step explanation:
The student asked for the equation in the form y = kx, which represents a direct variation where y varies directly as x. This means that as x increases or decreases, y does so in proportion to the constant k. The options given are all examples of this type of relationship, with k taking specific values: 1/3, 2/3, 3, and 4 respectively.
The question seems to be about understanding direct variation and the general form of linear equations which is y = b + mx, where b is the y-intercept and m is the slope of the line. However, in the context of direct variation, there is no y-intercept, and the equation simplifies to y = kx.
As an example, y = 9 + 3x is a linear equation with a y-intercept of 9 and a slope of 3. This is not a direct variation because of the non-zero y-intercept, unlike the options provided to the student, which all demonstrate direct variation with a y-intercept of zero.