Lesson 2: Practice Problems

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 $y = 4 x$ . 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.
distance (cm)
weight (newtons)
$20$
$28$
$55$
$140$
$1$
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 From Unit 2 Lesson 15

Describe how you can tell whether a line’s slope is greater than 1, equal to 1, or less than 1.