Project 5. Project: Biking in Kansas and Alaska.
In this project, we’re going to think about what makes a relationship linear or not linear. Each question is worth two points.
(a)
This is a graph of a linear relationship. Looking at it, what about it tells you that it is linear?
(b)
Here is a table of some of the points represented on the above graph. This data also represents a linear relationship. Without graphing, how can you tell that this relationship is linear?
x |
y |
-6 |
5 |
-3 |
3 |
0 |
1 |
3 |
-1 |
6 |
-3 |
(c)
Friends Jacob and Mike like to bike. For a math conference, the two traveled to Kansas and decided to go on a bike ride one evening. Mike enjoys tracking his data and so took note of his distance traveled at regular intervals. Here is a table of Mike’s time and mileage:
Time biked (in minutes) |
Distance traveled (in miles) |
10 |
2 |
20 |
4 |
30 |
6 |
40 |
8 |
50 |
10 |
Does this table represent a linear relationship? Give some supporting computations OR write a sentence to support your answer.
(d)
Jacob is more absent minded in tracking his mileage over time, and so took note of his distance traveled sporadically. Here is a table of Jacob’s time and mileage:
Time biked (in minutes) |
Distance traveled (in miles) |
7 |
1.4 |
12 |
2.4 |
20 |
4 |
35 |
7 |
54 |
10.8 |
Does this table represent a linear relationship? Give some supporting computations OR write a sentence to support your answer.
(e)
After returning home to Alaska, the friends decide to go on another ride. This bike ride was on a trail in the foothills of the Chugach Mountains. Again, Mike took note of his distance traveled at regular intervals Here is a table of Mike’s time and mileage:
Time biked (in minutes) |
Distance traveled (in miles) |
10 |
2.3 |
20 |
4 |
30 |
5.2 |
40 |
6 |
50 |
8 |
Does this table represent a linear relationship? Give some supporting computations OR write a sentence to support your answer.
(f)
Again, Jacob is absent minded in tracking his mileage over time, and so took note of his distance traveled sporadically. Here is a table of Jacob’s time and mileage:
Time biked (in minutes) |
Distance traveled (in miles) |
11 |
2.5 |
20 |
4 |
25 |
4.8 |
43 |
7 |
65 |
10.5 |
Does this table represent a linear relationship? Give some supporting computations OR write a sentence to support your answer.
(g)
Slope is \(\frac{\text{change in y values}}{\text{change in x values}}\text{.}\) If the first columns of the four tables above represent x values and the second columns represent y values, find the unit of the slope. Your answer should be a unit, like ft⁄s or in2, not a number.
(h)
(1 point extra credit): Consider your answer to the previous question. What does this unit represent? Your answer can be one word.
