Slope and Intercept Practice- Adv
Name___________________ Period_____
Step 1: Observe
Look at the graph on the bottom of this page.
Be silent and stare at this image for at least one minute. Try to notice something different every few seconds.
Step 2: Describe
Be sure to describe what you see. Don’t name it.
My eyes see…
How could you relate this graphic to what we have been learning about in class?
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Part A- In Context
Interpret slope & y-intercept
1.)
Using the graph above, what does the y-intercept represent in
the context of the situation?
2.) The table below shows the cost of renting a car. The company charges a daily rate for renting the car as
well as a one-time fee for insurance.
Days (d)
1
2
3
4
a.) What is the cost per day of renting a car?
b.) What is the insurance fee?
2
Cost (c)
70
115
160
205
3.) A taxi company charges an initial fee as well as a constant fee per mile traveled. This relationship is
represented in the graph below.
a. What is the initial fee charged by the taxi company?
b. What is the cost per mile
2.) The following representations of data express the speed of two different trains:
Train 1:
Train 2: Y = 400x, where x represents the hours traveled and y represents the total kilometers traveled.
Which train is traveling faster? How do you know?
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Part B- Interpreting Rates of Change
3.) If Amanda’s height can be represented by the equation
y = 3x+ 40, which of the following equations could represent Rachel’s
height?
a. Y = 3x + 60
b. Y = 1/3x + 50
c. Y = 1/3x + 25
d. Y = 3x + 25
4.) Which of the following has a greater rate of change, the equation or the graph? Justify your answer.
Y = 4/3 X - 1
Which has the greater y-intercept? How do you know?
5.) The cost of renting a car from two different companies is expressed in the following graph and equation.
Which of the following has the greater initial cost? Which of the companies has a greater rate of
change? How do you know?
Alamo
Enterprise Y = 0.5x + 28
6.) What is the meaning of the rate of change in the context of
the problem?
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7.) What is the meaning of the y-intercept on the graph?
Compare Slope & Y-Intercept between Equation and Graph
1.) Which of the following representations of data has a greater rate of change? Explain how you know.
(2 points)
Representation 1:
Representation 2:
Y = 3x – 2
2.) Which of the following representations of data has a greater rate of change? Explain how you know. (2
points)
Representation 1:
Y = -4x + 2
Representation 2:
3.) Using the representations of data above, which of the following has a greater initial value?
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Part C- Slope From a Table
1. Label your table with x and y.
2. Write the slope/rate of change formula.
3. Plug in the appropriate values and find your slope/rate of change.
4. Write the slope intercept formula.
5. Plug in values for y (from the table), m (your answer to step 3), and x (from the table).
6.
Solve for b, which is your y-intercept and “initial value.”
Notes
- The ___________ is the same thing as the rate _______ ______________.
- The y-_______________ is the same thing as
____________________________________.
- The formula for slope-intercept form of an equation is ____________________.
Examples
Rate of Change
Rate of Change
Initial Value
Initial Value
Slope-Intercept form
Slope-Intercept form
Which expression best represents the following situation?
The total cost of a trip to the movies for a family was $9 per ticket plus $20 for snacks.
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A. 20t - 9
B. 9 + t x 20
C. 9t - 20
D. 9t + 20
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Practice or Home Learning (depends on what you get done in class )
Rate of Change
Rate of Change
Initial Value
Initial Value
Slope-Intercept form
Slope-Intercept form
Rate of Change
Rate of Change
Initial Value
Initial Value
Slope-Intercept form
Slope-Intercept form
The table shows the distance that Mr.Stakus travels
during a week. Find the rate of change.
Amanda is selling cookies. The table shows the
relationship between the hours spent selling the number
of cookies that remain. Find the rate of change.
Interpret its meaning.
Rate of Change
Rate of Change
Initial Value
Initial Value
Slope-Intercept form
Slope-Intercept form
Time (days)
X
Distance
(miles)
Y
3
7
174
406
Hours
X
Cookies
Y
8
0
3
5
100
40
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Part C- Change in Variables
Name___________________ Per_______
In the equation y = 3x + 4, if the slope was changed from 3 to 5 describe, in your own words, the
change that would occur on the graph.
The graph below represents the equation y = -4/5x + 3. Which describes how this graph would need
to be changed to represent the equation y = -4/5x
a.
b.
c.
d.
The slope of the graph would need to become steeper
The slope of the graph would need to become less steep
Each point would need to be shifted up 3 units
Each point would need to be shifted down 3 units
The table shows the amount of money a Booster Club made washing cars for a fundraiser. The amount
of money earned can be expressed using y = 8x. This is shown in the table below. If another club held
a carwash and their profit can be represented by the equation y = 6x + 10, which values would be the
same in their table?
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The environmental science teacher at McMain High School is conducting an experiment that tracks the
temperature of water over time. Data from her experiment is recorded in the table below.
If the initial water temperature was 35 degrees Celsius, how would the graph change?
a. The slope of the line would become steeper
b. The slope of the line would become less steep
c. The line would move up on the graph
d. The line would move down on the graph
Which equation matches the statement “as the value of x increases the value of y decreases?”
Show all of your work to prove that you are correct. (Make a graph or table)
a. y = 3x – 1
b. y = 1x – 2
c. y = -2x
d. y = ½x
Which of the following statements is true if the equation y = 2x + 5 is changed to y = 2x – 3
A.
B.
C.
D.
The slope will become steeper
The line will shift down
The slope will stay the same
Nothing will change
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