Lesson 2
Representing Proportional Relationships
Let's graph proportional relationships.
Problem 1
The tortoise and the hare are having a race. After the hare runs 16 miles the tortoise has only run 4 miles.
The relationship between the distance \(x\) the tortoise “runs” in miles for every \(y\) miles the hare runs is \(y=4x\). Graph this relationship.
Problem 2
The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched.
- Complete the table.
- Describe the scales you could use on the \(x\) and \(y\) axes of a coordinate grid that would show all the distances and weights in the table.
| distance (cm) | weight (newtons) |
|---|---|
| 20 | 28 |
| 55 | |
| 140 | |
| 1 |
Problem 3
Students are selling raffle tickets for a school fundraiser. They collect $24 for every 10 raffle tickets they sell.
- Suppose \(M\) is the amount of money the students collect for selling \(R\) raffle tickets. Write an equation that reflects the relationship between \(M\) and \(R\).
- Label and scale the axes and graph this situation with \(M\) on the vertical axis and \(R\) on the horizontal axis. Make sure the scale is large enough to see how much they would raise if they sell 1000 tickets.
Problem 4
Describe how you can tell whether a line’s slope is greater than 1, equal to 1, or less than 1.