# Lesson 5

Equations and Their Graphs

### Problem 1

Select all the points that are on the graph of the equation $$4y-6x=12$$.

A:

$$(\text-4,\text-3)$$

B:

$$(\text-1,1.5)$$

C:

$$(0,\text-2)$$

D:

$$(0,3)$$

E:

$$(3,\text-4)$$

F:

$$(6,4)$$

### Problem 2

Here is a graph of the equation $$x+3y = 6$$.

Select all coordinate pairs that represent a solution to the equation.

A:

$$(0, 2)$$

B:

$$(0, 6)$$

C:

$$(2, 6)$$

D:

$$(3, 1)$$

E:

$$(4, 1)$$

F:

$$(6, 2)$$

### Problem 5

During the month of August, the mean of the daily rainfall in one city was 0.04 inches with a standard deviation of 0.15 inches. In another city, the mean of the daily rainfall was 0.01 inches with a standard deviation of 0.05 inches.

Han says that both cities had a similar pattern of precipitation in the month of August. Do you agree with Han? Explain your reasoning.

### Solution

(From Unit 1, Lesson 13.)

### Problem 6

In a video game, players form teams and work together to earn as many points as possible for their team. Each team can have between 2 and 4 players. Each player can score up to 20 points in each round of the game. Han and three of his friends decided to form a team and play a round.

Write an expression, an equation, or an inequality for each quantity described here. If you use a variable, specify what it represents.

1. the allowable number of players on a team
2. the number of points Han's team earns in one round if every player earns a perfect score
3. the number of points Han's team earns in one round if no players earn a perfect score
4. the number of players in a game with six teams of different sizes: two teams have 4 players each and the rest have 3 players each
5. the possible number of players in a game with eight teams

### Solution

(From Unit 2, Lesson 1.)

### Problem 7

A student on the cross-country team runs 30 minutes a day as a part of her training.

Write an equation to describe the relationship between the distance she runs in miles, $$D$$, and her running speed, in miles per hour, when she runs:

1. at a constant speed of 4 miles per hour for the entire 30 minutes
2. at a constant speed of 5 miles per hour the first 20 minutes, and then at 4 miles per hour the last 10 minutes
3. at a constant speed of 6 miles per hour the first 15 minutes, and then at 5.5 miles per hour for the remaining 15 minutes
4. at a constant speed of $$a$$ miles per hour the first 6 minutes, and then at 6.5 miles per hour for the remaining 24 minutes
5. at a constant speed of 5.4 miles per hour for $$m$$ minutes, and then at $$b$$ miles per hour for $$n$$ minutes

### Solution

(From Unit 2, Lesson 2.)

### Problem 8

In the 21st century, people measure length in feet and meters. At various points in history, people measured length in hands, cubits, and paces. There are 9 hands in 2 cubits. There are 5 cubits in 3 paces.

1. Write an equation to express the relationship between hands, $$h$$, and cubits, $$c$$.
2. Write an equation to express the relationship between hands, $$h$$, and paces, $$p$$.

### Solution

(From Unit 2, Lesson 3.)

### Problem 9

The table shows the amount of money, $$A$$, in a savings account after $$m$$ months.

Select all the equations that represent the relationship between the amount of money, $$A$$, and the number of months, $$m$$.

number of months dollar amount
5 1,200
6 1,300
7 1,400
8 1,500
A:

$$A = 100m$$

B:

$$A = 100(m - 5)$$

C:

$$A - 700 = 100m$$

D:

$$A - 1,\!200 = 100m$$

E:

$$A = 700 + 100m$$

F:

$$A = 1200 + 100m$$

G:

$$A = 1,\!200 + 100(m - 5)$$