Final answer:
The y-intercept of a linear function with a slope of 2/3 passing through (3,6) is (0,4). This is found by using the point-slope form of a linear equation and plugging in the known values.
Step-by-step explanation:
The student's question asks to find the y-intercept of a linear function with a given slope of 2/3 that passes through the point (3,6). To find the y-intercept, we can use the point-slope form of a straight line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Substituting the given point (3,6) and the slope 2/3 into the equation, we have:
y - 6 = (2/3)(x - 3).
Expanding this equation to find y when x is 0 gives us the y-intercept:
y = (2/3)(0 - 3) + 6
y = (2/3)(-3) + 6
y = -2 + 6
y = 4.
So, the y-intercept is at the point (0,4), which corresponds to option A. Therefore, the correct answer to the student's question is A. (0,4).