Comparing linear functions
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Elizabeth starts out 5 miles away from school and walks away from school at 3 miles per hour. So she's already 5 miles away. And she's going to walk even further away at 3 miles per hour. The table below shows how far some other students are from school at various times. Each person is moving at a constant speed starting at time is equal to 0. Which students started out farther from school than Elizabeth? Select all that apply. So essentially, we need to figure out where these students were at time equals 0. So we know where they were at time 1, 2, and 3. And so let's think about their rate towards or away from school. And remember, this is distance from school. As we increase-- as we go from hour 1 to hour 2, Gordon gets 2 miles closer. So his distance to school is decreasing. So where was he at time equals 0? I'll put time equals 0 up here because I don't have any-- actually, I'll put it right here. I'll try to squeeze it into the chart. So where was he at time equals 0? Well, he would have been 2 miles further. So he would have been 6 miles away. Notice that it's consistent. In the first hour, he would have gotten 2 miles closer to school. Then the next hour, he would have gotten 2 miles even closer. And then the third hour, he actually gets 2 miles closer. And he actually gets to school. So Gordon started out 6 miles away at t equals 0. So Gordon did start out farther from school than Elizabeth. So we can circle Gordon. He meets the conditions. Now let's think about Giovanni. So at time 1, he's 5 miles away from school. Then at 1 hour, he's 5 miles away. After 2 hours, he's 6 miles away. So he's getting further from school. So this is a plus 1. And then after another hour, he is 7 miles away. So every hour that goes by, he's a mile further. He's going 1 mile an hour away from school. So where was he at time equal 0? Well, he would have been a mile closer to school relative to time equal 1. So he would have been 4 miles away. So he did not start out farther than Elizabeth, who started out 5 miles away. Now let's look at Hannah. Hannah, at every time, is just exactly 5 miles away from school. So she's napping or something. She is not actually moving. She started out napping at exactly the same distance as Elizabeth, but she did not start out farther from school than Elizabeth. So Hannah does not meet the criteria. Now let's look at Alberto. At time equals 1, he is 9 miles from school. And then after 1 hour, he gets a mile and 1/2 further from school. After another hour, he gets a mile and 1/2 even further. So where was he at time equals 0? Well, he would have been a mile and 1/2 closer to school. So 9 minus 1.5 is-- he would have been 7 and 1/2 miles away. So even though he is going away from-- well, he definitely started further from school than Elizabeth. Elizabeth started out 5 miles away. Alberto started off 7 and 1/2 miles away and is going even further and further and further. So the two students that start out farther from school than Elizabeth are Gordon and Alberto.