Final answer:
To have an equation intersect with Priya's equation exactly once, change either the slope or the y-intercept. For example, y = -3/2x - 7 has a different slope from Priya's, ensuring one point of intersection. If both have the same slope but different y-intercepts, the lines would be parallel.
Step-by-step explanation:
To write an equation with exactly one solution in common with Priya's equation, we just need to alter either the slope or the y-intercept slightly, while making sure the two lines are not parallel. Priya's equation is y = -1/2x - 7, which has a slope of -1/2 and a y-intercept of -7. A simple way to ensure one point of intersection is to write an equation with the same slope but a different y-intercept or a different slope but the same y-intercept. If we take the latter approach, an example might be y = -3/2x - 7. This equation has a different slope, which means they will intersect at one point. However, if both equations had the same slope, they would be parallel and would either never intersect (if their y-intercepts are different) or they would be the same line (if their y-intercepts are the same).