Final answer:
If two lines have the same slope but different y-intercepts, they are parallel and do not intersect. Lines with the same slope and y-intercept overlap entirely. Line A and B, with different slopes, are not parallel and will intersect somewhere.
Step-by-step explanation:
When determining the relationship between two lines, if the slopes are the same, this typically indicates that the lines are parallel and thus do not intersect. However, the true relationship depends on their y-intercepts. If two lines have the same slope but different y-intercepts, they are parallel and will never intersect. On the other hand, if they have the same slope and the same y-intercept, they overlap completely and are called coincident lines.
In the case of Line A with a slope of -4.7 and Line B with a slope of 12.0, we can conclude that these two lines are not parallel, and they will intersect at some point because their slopes are different. The point of intersection would depend on their respective y-intercepts and can be found by solving the two equations of the lines simultaneously.
So for the student's question, the correct answer is B: No, the lines are parallel, assuming the lines have different y-intercepts. If the slopes are the same and y-intercepts are also the same, then the lines coincide.