Question

I need help with this topic

Answer 1

Let's go through these, sentence by sentence:

a. Henry is driving at a constant speed.

If the y-axis represents the speed of Henry's car, this portion of the graph should be a straight horizontal line, as his speed doesn't change at all. This already eliminates the first and second options.

He then slows down to pass an accident. After passing it, he goes back to his original speed and continues driving at that speed.

We should see a downward-sloped line segment during the period when he slows down, and then an upward-sloped line segment during the time where he speeds up. Graphically, this would look like a V. Finally, the graph would again become a straight horizontal line as he returned to and maintained his original speed. Graph #4 is the only one which represents this description.

b. Teresa is driving to work. She drives at a constant speed for several miles, then stops to pick up breakfast.

On all of the graphs of this situation, the y-axis represents Teresa's distance to work. We have to be careful here, because the further she drives, the further down the graph goes. The y-coordinate starts at some positive fixed position (the total distance to work) and works its way down to 0.

There's only one graph which represents this scenario - a downwards trend - and that's graph #3.