Final answer:
The correct equation of the line through the point (0, 3) with a slope of 2/3 is derived using the point-slope form and then transformed to standard form, resulting in 2x - 3y = -9 (option B).
Step-by-step explanation:
The question is asking to find the equation of a line that passes through the point (0, 3) with a slope m = 2/3. To determine the correct equation among the given options, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Since the line passes through (0, 3), we can substitute x1 = 0 and y1 = 3, and the slope m = 2/3 into the point-slope form to get the equation y - 3 = (2/3)(x - 0), which simplifies to y = (2/3)x + 3. Now, we need to convert this equation into the standard form, Ax + By = C, where A, B, and C are integers. Multiplying both sides by 3 to eliminate the fraction gives us 3y = 2x + 9. Bringing all terms to one side gives us 2x - 3y = -9, which corresponds to option B. Therefore, the correct equation of the line is 2x - 3y = -9.