# Equations and Their Graphs

ID: zofab-mufuh
Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2

27 questions

# Equations and Their Graphs

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##### Problem 1

1) Select all the points that are on the graph of the equation ﻿$4y - 6x = 12$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) (-4, -3) b) (-1, 1.5) c) (0, -2) d) (0, 3) e) (3, -4) f) (6, 4)

Show Work
##### Problem 2

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

2) Select all coordinate pairs that represent a solution to the equation. Write each corresponding letter in the answer box and separate letters with commas.

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.

8) Do you agree with Han?

a)

Yes

b)

No

c)

##### 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.

10) the allowable number of players, ﻿$p$﻿, on a team

11) If you used a variable, specify what it represents. If not, write "n/a".

12) the number of points, ﻿$S$﻿, Han's team earns in one round if every player earns a perfect score

13) If you used a variable, specify what it represents. If not, write "n/a".

14) the number of points, ﻿$S$﻿, Han's team earns in one round if no players earn a perfect score

15) If you used a variable, specify what it represents. If not, write “n/a”.

16) the number of players, ﻿$p$﻿, in a game with six teams of different sizes: two teams have 4 players each and the rest have 3 players each

17) If you used a variable, specify what it represents. If not, write “n/a”.

18) the possible number of players, ﻿$p$﻿, in a game with eight teams

19) If you used a variable, specify what it represents. If not, write “n/a”.

##### 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:

20) at a constant speed of 4 miles per hour for the entire 30 minutes

21) at a constant speed of 5 miles per hour the first 20 minutes, and then at 4 miles per hour the last 10 minutes

22) 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

23) 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

24) 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.

25) Write an equation to express the relationship between hands, ﻿$h$﻿, and cubits, ﻿$c$﻿.

26) Write an equation to express the relationship between hands, ﻿$h$﻿, and paces, ﻿$p$﻿.

##### Problem 9

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

﻿$\begin{array}{|c|c|} \hline \\[-1em] \textbf{number of months} & \textbf{dollar amount} \\[-1em] \\ \hline \\[-1em] 5 & 1,200 \\[-1em] \\ \hline \\[-1em] 6 & 1,300 \\[-1em] \\ \hline \\[-1em] 7 & 1,400 \\[-1em] \\ \hline \\[-1em] 8 & 1,500 \\[-1em] \\ \hline \end{array}$﻿

Select all the equations that represent the relationship between the amount of money, ﻿$A$﻿, and the number of months, ﻿$m$﻿. Write each corresponding letter in the answer box and separate letters with commas.

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) ﻿$A = 1,200 + 100(m-5)$﻿