Vicky is solving an equation where both sides are linear expressions. She sets each linear expression equal to y and graphs the resulting system. If the y-intercepts of the graphs are the same but the slopes are different, what is the greatest possible number of intersections for these graphs?

The graphs are lines with the same y-intercept, so they both pass through the same point on the y-axis. Because their slopes are different, they are not the same line and meet at only that one point. Therefore, the greatest possible number of intersections is one, choice B.

AI-written and checked against the verified answer.