8.
The graph represents a distance run.
The point (0, 0) means (0 minutes, 0 miles).
That means that at time zero, the horses had run 0 miles.
In other words, at time zero they were just about to start running, but they had not run yet, so the distance they had run so far was 0.
9.
Each graph is a straight line. Every mile in each graph takes the same time to run. Let's look for easy points to read on graph A. At 4 minutes, horse A had run 1 mile. At 8 minutes, it had run 2 miles. From 4 minutes to 8 minutes it's 4 minutes. It went from 1 mile to 2 miles in 4 minutes, so horse A ran 1 mile in 4 minutes.
Now we do the same for horse B. We first look for two points that are easy to read on graph B. I see (5, 2) and (10, 4). The difference in miles is: 4 - 2 = 2; the difference in minutes is: and 10 - 5 = 5. Horse B ran 2 miles in 5 minutes, so it runs 1 mile in 2.5 minutes.
10.
Both horses start at (0, 0), so for both horses, the y-intercept is 0.
Each equation only has a slope.
From the problem above, we have for horse A, 1 mile per 4 minutes, or a slope of 1/4. For horse B we have 1 mile per 2.5 minutes, or a slope of 2/5.
Horse A: y = (1/4)x
Horse B: y = (2/5) x
11.
Use each equation above. Let x = 12, and solve for y.
Horse A: y = (1/4)x = (1/4) * 12 = 3
Horse B: y = (2/5)x = (2/5) * 12 = 4.8
Horse A travels 3 miles, and horse B travels 4.8 miles in 12 minutes.
12.
Since you see that horse B is faster than horse A, and the graph of B is above the graph of A, a horse faster than horse B would have a graph above line B that is steeper than line B. Start a straight line at (0, 0), go up to the right, and make sure this line is above line B.
13.
No. While the train is traveling at a constant 170 mph, the graph is a straight line representing a proportional relationship between time and distance, but while the train is accelerating from 0 mph to 170 mph, and while the train slows down, the relationship between distance traveled and time is not proportional.
15.a.
1 DVD costs $5.
2 DVDs cost $10.
3 DVDs cost $15.
4 DVDs cost $20.
Plot the points (0, 0), (1, 5), (2, 10), (3, 15), (4, 20).
The draw a straight line through them.
15.b.
Pick point (7, 35).
This point means that 7 DVDs cost $35.
