Question

practice it! select the statement that accurately interprets the distance - time graph. karina rode her bike east from her home up a steep hill. after a while, the slope of the hill decreased. once she reached the top of the hill, she raced down the other side. karina took her dog for a walk to the park. she set off slowly and then increased her pace. at the park, karina turned around and walked slowly back home. karina took the city bus to the library. when she got on, the bus traveled at a constant speed. the bus stopped to pick someone else up. then the bus stopped at the library and karina got off. karina went for a jog. she ran at a steady pace for some distance. at the end of her road, she bumped into a friend and her pace slowed to a walk. when karina left her friend, she walked quickly back home. graph: distance from home (y - axis) vs time (x - axis), with a line starting at origin, rising steeply, then less steeply, then falling steeply to origin

Explanation:

1. Analyze the first option: When going up a hill with decreasing slope, the speed (slope of distance - time graph) decreases, but the distance from home should keep increasing. However, the graph has a segment with a shallower slope (lower speed) while distance from home still increases, but then a steep decrease (racing down). But the key is that when going down the hill, the distance from home should decrease, but the first part's description of the slope change doesn't match the graph's structure as well as the correct option.
2. Analyze the second option: If she walked slowly back home, the slope (speed) on the way back should be small (shallow slope), but in the graph, the way back has a steep slope (fast speed), so this is incorrect.
3. Analyze the third option: If the bus stopped, the distance - time graph should have a horizontal segment (constant distance as time passes). But the graph has no horizontal segments, so this is incorrect.
4. Analyze the fourth option: She ran at a steady pace (steep slope) first, then slowed to a walk (shallower slope) while still moving away from home (distance increasing), then walked quickly back home (steep slope, distance decreasing). This matches the graph's structure: a steep increase, then a shallower increase, then a steep decrease.

Answer:

Karina rode her bike east from her home up a steep hill. After a while, the slope of the hill decreased. Once she reached the top of the hill, she raced down the other side.