Transcript Finding Intercepts, Changing Slopes y-Intercepts, Meaning of Slope, Problem Solving

Let’s Get Ready
To Play Some . . .
JEOPARDY
JEOPARDY
JEOPARDY
Jeopardy Board
Final Jeopardy
Finding
Intercepts
Changing Slopes
and y-intercepts
Meaning of
the Slope and
Intercepts
100
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200
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300
300
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400
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500
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500
Problem Solving
Finding Intercepts 100
What are the x- and y-intercepts of the function
graphed below?
Board
Answer
Finding Intercepts 100
What are the x- and y-intercepts of the function
graphed below?
F (4, 0) and (5, 0)
(0 ,5 )
G (4, 0) and (0, 5)
(4 ,0 )
H (0, 4) and (5, 0)
J (0, 4) and (0, 5)
Board
Finding Intercepts 200
Which coordinate points represent the x- and yintercepts of the graph shown below?
Board
Answer
Finding Intercepts 200
Which coordinate points represent the x- and yintercepts of the graph shown below?
F
G
H
J
(0, −4) and (6, 0)
(−4, 0) and (0, 6)
(6, 0) and (−4, 0)
(0, 6) and (0, −4)
Board
(0 ,6 )
(-4 , 0 )
Finding Intercepts 300
What is the y-intercept of the function
f (x) = 3(x − 2)?
Board
Answer
Finding Intercepts 300
What is the y-intercept of the function
f (x) = 3(x − 2)?
F
G
H
J
3
1
−2
−6
y = mx + b
slope
m = __________
y-intercept
b = __________
f (x) = 3(x − 2)
f (x) = 3x − 6
Board
Simplify
Finding Intercepts 400
What are the coordinates of the y-intercept of the
line represented by the equation 4x + 2y = 10?
Board
Answer
Finding Intercepts 400
What are the coordinates of the y-intercept of the
line represented by the equation 4x + 2y = 10?
A
(0, 2)
B
(0,
5
)
2
C
(0, 5)
D
(0, 10)
Board
y = mx + b
slope
m = __________
y-intercept
b = __________
4x + 2y = 10 Solve for y
-4x
-4x
2y = -4x + 10
2
2
2
y = -2x + 5
Finding Intercepts 500
What are the coordinates of the x-intercept of
the equation −3y = 8 − 2x?
Board
Answer
Finding Intercepts 500
What are the coordinates of the x-intercept of
the equation −3y = 8 − 2x?
F
G
H
J
Solve for y
-3y
=
8
–
2x
(−2, 0) -3 -3 -3
8
8 2
(0, − )
y  x
3
2
3 3
( , 0)
3
Check:
(4, 0)
-3y
=
8
–
2x
(x, y)
-3(0) = 8 – 2(4)
Board


Changing Slopes and y-intercepts 100
Which best describes the effect on the graph of f
(x) = 4x + 8 if the y-intercept is changed to −3?
F The slope decreases.
G The new line passes through the origin.
H The x-intercept increases.
J The y-intercept increases.
Board
Answer
Changing Slopes and y-intercepts 100
Which best describes the effect on the graph of f
(x) = 4x + 8 if the y-intercept is changed to −3?
F The slope decreases.
G The new line passes through the origin.
H The x-intercept increases.
J The y-intercept increases.
Slope
Origin?
x-intercept
y-intercept
4x + 8 4x – 3
4
4
no
no
(-2, 0) (3/4, 0)
(0, 8) (0, -3)
Board
Changing Slopes and y-intercepts 200
What will happen to the slope of line p if the
line is shifted so that the y-intercept increases
and the x-intercept remains the same?
F The slope will change from
positive to negative.
G The slope will change from
negative to positive.
H The slope will increase.
J The slope will decrease.
Board
Answer
Changing Slopes and y-intercepts 200
What will happen to the slope of line p if the
line is shifted so that the y-intercept increases
and the x-intercept remains the same?
F The slope will change from
positive to negative.
G The slope will change from
negative to positive.
H The slope will increase.
J The slope will decrease.
Board
Changing Slopes and y-intercepts 300
Given the function y = 3.54x − 54.68, which
statement best describes the effect of increasing
the y-intercept by 33.14?
A
B
C
D
The new line is parallel to the original.
The new line has a greater rate of change.
The x-intercept increases.
The y-intercept decreases.
Board
Answer
Changing Slopes and y-intercepts 300
Given the function y = 3.54x − 54.68, which
statement best describes the effect of increasing
the y-intercept by 33.14?
A
B
C
D
The new line is parallel to the original.
The new line has a greater rate of change.
The x-intercept increases.
The y-intercept decreases.
Board
Changing Slopes and y-intercepts 400
The line represented by the equation y = x + 3 is
graphed below.
Which of the following best describes the
effect on the graph when the slope is doubled?
A The y-intercept increases.
B The y-intercept decreases.
C The x-intercept increases.
D The x-intercept decreases.
Board
Answer
Changing Slopes and y-intercepts 400
The line represented by the equation y = x + 3 is
graphed below.
Which of the following best describes the
effect on the graph when the slope is doubled?
A The y-intercept increases.
B The y-intercept decreases.
C The x-intercept increases.
D The x-intercept decreases.
y = mx + b
slope
m = __________
y-intercept
b = __________
Board
y = __x
1 +3
12=2
m = __________
3
b = __________
y = 2x + 3
Changing Slopes and y-intercepts 500
The graph of a line is shown below.
If the slope of this line is multiplied by −1 and the
y-intercept decreases by 2 units, which linear
equation represents these changes?
A y = −2x + 1
B y = −x + 1
C y = −x − 1
D y=−x−1
Board
Answer
Changing Slopes and y-intercepts 500
The graph of a line is shown below.
If the slope of this line is multiplied by −1 and the
y-intercept decreases by 2 units, which linear
equation represents these changes?
A y = −2x + 1
B y = −x + 1
C y = −x − 1 b = _______
3 –2 =1
2
D y=−x−1
 -1 = -2
y = mx + b
slope
m = __________
y-intercept
b = __________
Board
1
m = _______
y = -2x + 1
Meaning of the Slope and Intercepts 100
A toy car travels 40 feet in 8 seconds. How
fast did it travel?
Board
Answer
Meaning of the Slope and Intercepts 100
A toy car travels 40 feet in 8 seconds. How
fast did it travel?
change in dis tan ce
slope 
change in time
traveled 40 feet
slope 
in 8 seconds
slope  5 ft / sec
Board
Meaning of the Slope and Intercepts 200
The table show the price a car repair shop
charges in labor. It includes a one time
garage fee plus an hourly rate. What is the
hourly rate?
Number Charge
of hours of labor
2
160
Board
Answer
3
210
4
260
8
460
Meaning of the Slope and Intercepts 200
The table show the price a car repair shop
charges in labor. It includes a one time
garage fee plus an hourly rate. What is the
hourly rate?
Number Charge
$50/hr
The hourly rate is _____________
$50/1hr = $50/hr
1 hr
$50/1hr = $50/hr
1 hr
$200/4hr = $50/hr
4 hr
Board
of hours of labor
2
160
3
210
4
260
8
460
$50
$50
$200
change in money
slope  hourly ch arg e 
change in time
Meaning of the Slope and Intercepts 300
The graph below shows the number of caramel apples
and the number of popcorn balls that the students in
the math club need to sell at their bake sale to raise
$200. Which of the following numbers represents the
maximum number of caramel-apple sales needed to
raise exactly $200?
A
B
C
D
50
40
25
20
Board
Answer
Meaning of the Slope and Intercepts 300
The graph below shows the number of caramel apples
and the number of popcorn balls that the students in
the math club need to sell at their bake sale to raise
$200. Which of the following numbers represents the
maximum number of caramel-apple sales needed to
raise exactly $200?
A
B
C
D
50
40
25
20
Board
Answer
Amount of water (m3)
Meaning of the Slope and Intercepts 300
The graph shows the amount of water in a
tank with a small leak in it. How fast is the
water leaking out of the tank in m3 per min
Board
Answer
Minutes
The water is leaking at
0.15 m3/min
_______
Amount of water (m3)
Meaning of the Slope and Intercepts 300
The graph shows the amount of water in a
tank with a small leak in it. How fast is the
water leaking out of the tank in m3 per min
m  hourly ch arg e
change in amt. of water

change in time
30 m3  24 m3
6 m3


40 min  0 min
40 min
= 3/20 m3/min
Board
= 0.15 m3/min
Minutes
Meaning of the Slope and Intercepts 400
The line segment on the graph shows the altitude of a landing
airplane from the time its wheels are lowered to the time it
touches the ground. Which of the following best describes the
slope of the line segment?
F The plane descends about 1 foot per 8 seconds.
G The plane descends about 8 feet per second.
H The plane descends about 1 foot per 2 seconds.
J The plane descends about 2 feet per second.
Board
Answer
Meaning of the Slope and Intercepts 400
The line segment on the graph shows the altitude of a landing
airplane from the time its wheels are lowered to the time it
touches the ground. Which of the following best describes the
slope of the line segment?
F The plane descends about 1 foot per 8 seconds.
G The plane descends about 8 feet per second.
H The plane descends about 1 foot per 2 seconds.
J The plane descends about 2 feet per second.
change in height
m
change in time
1500 ft
m
= 8 ft/sec
180sec
Board
Meaning of the Slope and Intercepts 500
What are the slope and y-intercept of a line that
contains the point (5, −1) and has the same
y-intercept as x − 3y = 6?
Board
Answer
Meaning of the Slope and Intercepts 500
What are the slope and y-intercept of a line that
contains the point (5, −1) and has the same
y-intercept as x − 3y = 6?
A m=
1
3
b=6
B m=5
b = −2
Board
C m=
1
5
b = −2
D m=3
b=6
x − 3y = 6
-x
-x Solve for y
-3y = -x + 6
-3
-3 -3
y = (1/3)x – 2
Problem Solving 100
Mike was driving his car at a constant speed of 50
miles per hour. Then he accelerated at a constant rate
for 7 seconds. What additional information is needed
to determine the speed of the car after 7 seconds?
A
B
C
D
The speed of the car prior to acceleration
The length of time Mike accelerated
The speed limit
The rate of acceleration
Board
Answer
Problem Solving 100
Mike was driving his car at a constant speed of 50
miles per hour. Then he accelerated at a constant rate
for 7 seconds. What additional information is needed
to determine the speed of the car after 7 seconds?
A
B
C
D
The speed of the car prior to acceleration
The length of time Mike accelerated
The speed limit
The rate of acceleration
Board
Problem Solving 200
Rinaldo’s school sold all of the tickets to a band
concert. The tickets cost $8 each. The auditorium
where the concert was held had 39 rows, with 56 seats
in each row. Which of the following is a correct
method for Rinaldo to calculate the total amount of
ticket sales?
F Rinaldo can multiply 56 by $8 and then add 39.
G Rinaldo can add 39 and 56 and then multiply by $8.
H Rinaldo can multiply 39 and 56 and then multiply
by $8.
J Rinaldo can add 56 and $8 and then multiply by 39.
Board
Answer
Problem Solving 200
Rinaldo’s school sold all of the tickets to a band
concert. The tickets cost $8 each. The auditorium
where the concert was held had 39 rows, with 56 seats
in each row. Which of the following is a correct
method for Rinaldo to calculate the total amount of
ticket sales?
F Rinaldo can multiply 56 by $8 and then add 39.
G Rinaldo can add 39 and 56 and then multiply by $8.
H Rinaldo can multiply 39 and 56 and then multiply
by $8.
J Rinaldo can add 56 and $8 and then multiply by 39.
Board
Problem Solving 300
As part of a classroom assignment, Kimberly was
given this geoboard to model the slope of 2
3
If the peg in the lower left-hand corner represents the
origin on a coordinate plane, where could Kimberly
place a rubber band to represent the given slope?
F From peg V to peg W
G From peg V to peg X
H From peg V to peg Y
J From peg V to peg Z
Board
Answer
Problem Solving 300
As part of a classroom assignment, Kimberly was
given this geoboard to model the slope of 2
3
If the peg in the lower left-hand corner represents the
origin on a coordinate plane, where could Kimberly
place a rubber band to represent the given slope?
F From peg V to peg W
G From peg V to peg X
H From peg V to peg Y
J From peg V to peg Z
Board
2 2

3 3
Problem Solving 400
Nikolay made a fruit drink composed of 36% orange
juice. The rest of the fruit drink was grape juice. If
Nikolay drank x ounces of the fruit drink, which
equation best represents y, the number of ounces of
grape juice he drank?
F y=
G y
9
25
16
= 25
Board
x
x
H y
J
9
= 16
y=
Answer
x
16
x
9
Problem Solving 400
Nikolay made a fruit drink composed of 36% orange
juice. The rest of the fruit drink was grape juice. If
Nikolay drank x ounces of the fruit drink, which
equation best represents y, the number of ounces of
grape juice he drank?
36% orange means 64% grape
F y=
G y
9
25
16
= 25
Board
x
x
H y
J
9
= 16
y=
x
16
x
9
Problem Solving 500
The function g(x) = 1.25 + 0.70(x − 1) represents the
charge for parking in the mall garage for x number of
hours. Which statement best represents the formula for
this charge?
A The charge consists of a set fee of $1.25 plus $0.70 for
every hour parked.
B The charge consists of a flat rate of $0.70 for every hour
parked.
C The charge consists of $1.25 for the first hour parked and
$0.70 for each additional hour.
D The charge consists of $1.25 for every hour parked plus a
set fee of $0.70.
Board
Answer
Problem Solving 500
The function g(x) = 1.25 + 0.70(x − 1) represents the
charge for parking in the mall garage for x number of
hours. Which statement best represents the formula for
this charge?
A The charge consists of a set fee of $1.25 plus $0.70 for
every hour parked.
B The charge consists of a flat rate of $0.70 for every hour
parked.
C The charge consists of $1.25 for the first hour parked and
$0.70 for each additional hour.
D The charge consists of $1.25 for every hour parked plus a
set fee of $0.70.
Board
Final Jeopardy Category
Board
Final Jeopardy Question
What is the y-intercept of
the function graphed below?
A
−24
B
−21
C
−18
D
−9
Answer
Final Jeopardy Answer
What is the y-intercept of
the function graphed below?
A
−24
14 7

4
2
B
−21 Slope = _________
C
−18
D
−9
-14
-4
Board
Final Jeopardy Answer
What is the y-intercept of
the function graphed below?
A
−24
14 7

4
2
B
−21 Slope = _________
C
−18
D
−9
-7
( 8 , 10)
-2
(0, -18)
One more time ________
-7
(4, -4)
-2
Board
(2, -11)