Final answer:
According to the description, the equation of the line is y = 3x + 9 based on the slope of 3 and the y-intercept of 9. However, none of the options provided in the question (A to E) matches this equation.
Step-by-step explanation:
To find the equation of the line in slope-intercept form, which is y = mx + b, we need to identify the slope (m) and the y-intercept (b). According to the provided data, the slope of the line is 3 because there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis. The y-intercept is given as 9, as this is the point where the line intersects the y-axis. Therefore, the equation of the line is y = 3x + 9.
However, looking at the options provided in the original question, none of them match our equation of y = 3x + 9. It's likely that there has been a typo or error either in the options given or in the description of the line. With the correct slope and y-intercept from the description, option B, y = 3x - 2, and option C, y = -3x - 2, don't match because they both have different y-intercepts; option A, y = -1/3x - 6, and option D, y = -1/3x - 2, don't match because they have different slopes and y-intercepts. Lastly, option E, y = -3x - 6, also has a different slope and y-intercept. Therefore, with the information provided, none of the options is correct.