Final answer:
The correct y-coordinate of point B based on the equation y = 9 + 3x is 3x + 9, hence the coordinates of B are (x, 3x + 9), which is not represented by any of the provided options.
Step-by-step explanation:
To find the coordinates of point B with a given equation y = 9 + 3x, we need to understand the form of the equation y = mx + b, where m represents the slope and b represents the y-intercept. The equation given indicates that the slope, m, is 3, and the y-intercept, b, is 9. To set up the equation to solve for y_2, also known as the y-coordinate of point B, if we have x represented as x, then we can substitute x into the equation to find y. Therefore, the y-coordinate y_2 is calculated as 3x + 9, which after multiplying by 2 on both sides simplifies to 2y_2 = 6x + 18. Solving for y_2, we get: y_2 = 3x + 9. Consequently, the coordinates of point B are (x, 3x + 9), which matches none of the options provided (a. (x, 2x + 42), b. (2x, x + 42), c. (x, x + 42), d. (2x, 2x + 42)).