# Warm Up - DanPrest

```GRAPHING LINEAR
EQUATIONS
Linear Equations
• Independent variable (x): the quantity that
changes based on values you choose
• Dependent variable (y): the quantity that is based
on the input values of the independent variable
Warm Up
Steps for creating linear equations:
2. Determine the known quantities.
3. Identify the slope and the y-intercept.
4. Substitute the slope and y-intercept into the
equation y=mx+b.
5. Graph the equation.
1. A local convenience store owner spent \$10 on pencils to resell
at the store. What is the equation that store’s revenue if each
pencil sells for \$0.50? Graph the equation using a table of values.
2. A taxi company in Atlanta charges \$2.50 per ride plus \$2 for
every mile driven. Write and graph the equation (using the slope
and y-intercept) that models this scenario.
3. Miranda gets paid \$300 a week to deliver groceries. She also
earns 5% commission on any orders she collects while out on her
delivery run. Write an equation that represents her weekly pay
and then graph the equation.
4. A Boeing 747 starts out a long flight with about 57,260 gallons
of fuel in its tank. The airplane uses an average of 5 gallons of
fuel per mile. Write an equation that models the amount of fuel in
the tank then graph the equation using a graphing calculator.
5. You can buy a 6-hour phone card for \$5, but the fine print says
that each minute you talk actually costs you 1.5 amount of time.
What is the equation that models the number of minute left on the
card compared with the number of minutes you actually talked?
What is the graph of this equation?
Warm Up
One form of the element beryllium, beryllium-11, has a half-life of about
14 seconds and decays to the element boron. A chemist starts out with
128 grams of beryllium-11. She monitors the element for 70 seconds.
1. What is the equation that models the amount of beryllium-11 over
time?
2. How many grams of beryllium-11 does the chemist have left after 70
seconds?
GRAPHING
EXPONENTIAL
EQUATIONS
Exponential Equations Review
• General form:
• Growth: the base is greater than 1
• Decay: the base is between 0 and 1
Compound Interest
• A: initial value
• P: principle amount
• r: interest rate
• n: number of years
Compound Interest Cheat Sheet
Compounded…
n (number of times per year)
Year/annually
1
Semi-annually
2
Quarterly
4
Monthly
12
Weekly
52
Daily
365
1. If a pendulum swings to 90% of its height on each swing and
starts out at a height of 60 cm, what is the equation that models
this scenario? What is its graph?
2. The bacteria Streptococcus lactis doubles every 26 minutes in
milk. If a container of milk contains 4 bacteria, write an equation
that models this scenario and then graph the equation.
3. An investment of \$500 is compounded monthly rate of 3%.
What is the equation that models this situation? Graph the
equation.
Warm Up
```
The text passage contains a series of questions and problems related to graphing linear and exponential equations, along with some background information and steps for solving these types of problems.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Warm Up - DanPrest

```GRAPHING LINEAR
EQUATIONS
Linear Equations
• Independent variable (x): the quantity that
changes based on values you choose
• Dependent variable (y): the quantity that is based
on the input values of the independent variable
Warm Up
Steps for creating linear equations:
2. Determine the known quantities.
3. Identify the slope and the y-intercept.
4. Substitute the slope and y-intercept into the
equation y=mx+b.
5. Graph the equation.
1. A local convenience store owner spent \$10 on pencils to resell
at the store. What is the equation that store’s revenue if each
pencil sells for \$0.50? Graph the equation using a table of values.
2. A taxi company in Atlanta charges \$2.50 per ride plus \$2 for
every mile driven. Write and graph the equation (using the slope
and y-intercept) that models this scenario.
3. Miranda gets paid \$300 a week to deliver groceries. She also
earns 5% commission on any orders she collects while out on her
delivery run. Write an equation that represents her weekly pay
and then graph the equation.
4. A Boeing 747 starts out a long flight with about 57,260 gallons
of fuel in its tank. The airplane uses an average of 5 gallons of
fuel per mile. Write an equation that models the amount of fuel in
the tank then graph the equation using a graphing calculator.
5. You can buy a 6-hour phone card for \$5, but the fine print says
that each minute you talk actually costs you 1.5 amount of time.
What is the equation that models the number of minute left on the
card compared with the number of minutes you actually talked?
What is the graph of this equation?
Warm Up
One form of the element beryllium, beryllium-11, has a half-life of about
14 seconds and decays to the element boron. A chemist starts out with
128 grams of beryllium-11. She monitors the element for 70 seconds.
1. What is the equation that models the amount of beryllium-11 over
time?
2. How many grams of beryllium-11 does the chemist have left after 70
seconds?
GRAPHING
EXPONENTIAL
EQUATIONS
Exponential Equations Review
• General form:
• Growth: the base is greater than 1
• Decay: the base is between 0 and 1
Compound Interest
• A: initial value
• P: principle amount
• r: interest rate
• n: number of years
Compound Interest Cheat Sheet
Compounded…
n (number of times per year)
Year/annually
1
Semi-annually
2
Quarterly
4
Monthly
12
Weekly
52
Daily
365
1. If a pendulum swings to 90% of its height on each swing and
starts out at a height of 60 cm, what is the equation that models
this scenario? What is its graph?
2. The bacteria Streptococcus lactis doubles every 26 minutes in
milk. If a container of milk contains 4 bacteria, write an equation
that models this scenario and then graph the equation.
3. An investment of \$500 is compounded monthly rate of 3%.
What is the equation that models this situation? Graph the
equation.
Warm Up
```
user
The text passage contains a series of questions and problems related to graphing linear and exponential equations, along with some background information and steps for solving these types of problems.

TYPE: MULTIPLE_QUESTIONS