Final answer:
To determine if two lines are parallel, compare their slopes. The line equations given are y = 5x + 3 and y = 9x - 33. Since the slopes are different, the lines are not parallel.
Step-by-step explanation:
To determine the value of x that will prove that line I is parallel to line m, we need to compare the slopes of the two lines. In the equation for line I, y = 5x + 3, the slope is 5. In the equation for line m, y = 9x - 33, the slope is 9. Since parallel lines have equal slopes, we can set the slopes of the two lines equal to each other and solve for x:
5 = 9
This equation does not have a solution, which means that there is no value of x that will prove that line I is parallel to line m. Therefore, option A) (5x + 3) is not the correct answer.
Option B) (9x - 33) is the correct answer because it represents the equation for line m, which has a different slope than line I, proving that the two lines are not parallel.