# Lesson 5

Equations and Their Graphs

- Let’s graph equations in two variables.

### Problem 1

Select **all** the points that are on the graph of the equation \(4y-6x=12\).

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

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

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

\((0,3)\)

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

\((6,4)\)

### Problem 2

Here is a graph of the equation \(x+3y = 6\).

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

\((0, 2)\)

\((0, 6)\)

\((2, 6)\)

\((3, 1)\)

\((4, 1)\)

\((6, 2)\)

### Problem 3

A theater is selling tickets to a play. Adult tickets cost $8 each and children’s tickets cost $5 each. They collect $275 after selling \(x\) adult tickets and \(y\) children’s tickets.

What does the point \((30, 7)\) mean in this situation?

### Problem 4

*Technology required. *Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks.

- Write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving.
- Graph your equation using graphing technology. Mark the point on the graph that represents the amount after 3 weeks.
- How many weeks does it take her to have $250 in her bank account? Mark this point on the graph.

### 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.

### 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.

- the allowable number of players on a team
- the number of points Han's team earns in one round if every player earns a perfect score
- the number of points Han's team earns in one round if no players earn a perfect score
- 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
- the possible number of players in a game with eight teams

### 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:

- at a constant speed of 4 miles per hour for the entire 30 minutes
- at a constant speed of 5 miles per hour the first 20 minutes, and then at 4 miles per hour the last 10 minutes
- 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
- 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
- at a constant speed of 5.4 miles per hour for \(m\) minutes, and then at \(b\) miles per hour for \(n\) minutes

### 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.

- Write an equation to express the relationship between hands, \(h\), and cubits, \(c\).
- Write an equation to express the relationship between hands, \(h\), and paces, \(p\).

### 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 |

\(A = 100m\)

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

\(A - 700 = 100m\)

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

\(A = 700 + 100m\)

\(A = 1200 + 100m\)

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