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Finding Intercepts

Changing Slopes and y-intercepts

Meaning of the Slope and

InterceptsProblem Solving

100 100 100 100

200 200 200 200

300 300 300 300

400 400 400 400

500 500 500 500

Final Jeopardy

Jeopardy BoardJeopardy Board

Board Answer

Finding Intercepts 100What are the x- and y-intercepts of the function graphed below?

Board

Finding Intercepts 100What are the x- and y-intercepts of the function graphed below?

F (4, 0) and (5, 0)G (4, 0) and (0, 5)H (0, 4) and (5, 0)J (0, 4) and (0, 5)

( , )0 5

( , )4 0

Board Answer

Finding Intercepts 200Which coordinate points represent the x- and y-intercepts of the graph shown below?

Board

Finding Intercepts 200

F (0, −4) and (6, 0)G (−4, 0) and (0, 6)H (6, 0) and (−4, 0)J (0, 6) and (0, −4)

Which coordinate points represent the x- and y-intercepts of the graph shown below?

( , )0 6

( , )-4 0

Board Answer

Finding Intercepts 300What is the y-intercept of the function f (x) = 3(x − 2)?

Board

Finding Intercepts 300What is the y-intercept of the function f (x) = 3(x − 2)?

F 3G 1H −2J −6

y = mx + b

f (x) = 3(x − 2)

m = __________slope

b = __________y-intercept

Simplify

f (x) = 3x − 6

Board Answer

Finding Intercepts 400What are the coordinates of the y-intercept of the line represented by the equation 4x + 2y = 10?

What are the coordinates of the y-intercept of the line represented by the equation 4x + 2y = 10?

Board

Finding Intercepts 400

5

2

A (0, 2)

B (0, )

C (0, 5)

D (0, 10)

y = mx + b

4x + 2y = 10

m = __________slope


Solve for y-4x -4x

2y = -4x + 102 2 2y = -2x + 5

Board Answer

Finding Intercepts 500What are the coordinates of the x-intercept of the equation −3y = 8 − 2x?

Board

Finding Intercepts 500What are the coordinates of the x-intercept of the equation −3y = 8 − 2x?

F (−2, 0)

G (0, − )

H ( , 0)

J (4, 0)

8

32

3

Solve for y-3y = 8 – 2x -3 -3 -3

8 2y x

3 3

Check: (x, y) -3y = 8 – 2x

-3(0) = 8 – 2(4)

Board Answer

Changing Slopes and y-intercepts 100Which 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

Changing Slopes and y-intercepts 100

y =

4x +

8

y =

4x –

3

4x + 8 4x – 3 Slope

Origin?

x-intercept

y-intercept

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.

4 4no no

(-2, 0) (3/4, 0)(0, 8) (0, -3)

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


Board

Changing Slopes and y-intercepts 200What 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 300Given the function y = 3.54x − 54.68, which statement best describes the effect of increasing the y-intercept by 33.14?

A The new line is parallel to the original.B The new line has a greater rate of change.C The x-intercept increases.D The y-intercept decreases.

Board

Changing Slopes and y-intercepts 300Given the function y = 3.54x − 54.68, which statement best describes the effect of increasing the y-intercept by 33.14?

A The new line is parallel to the original.B The new line has a greater rate of change.C The x-intercept increases.D The y-intercept decreases.

The line represented by the equation y = x + 3 is graphed below.Which of the following best describes theeffect 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


Board

Changing Slopes and y-intercepts 400The line represented by the equation y = x + 3 is graphed below.Which of the following best describes theeffect 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 + bm = __________slope


y = __x + 31m = __________

b = __________

1

3

2 = 2

y = 2x + 3

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 + 1B y = −x + 1C y = −x − 1D y = − x − 1

Board Answer


Board

Changing Slopes and y-intercepts 500The 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 + 1B y = −x + 1C y = −x − 1D y = − x − 1

y = mx + bm = __________slope


b = _______

m = _______

32

1 -1 = -2

– 2 = 1

y = -2x + 1

Board Answer

Meaning of the Slope and Intercepts 100

A toy car travels 40 feet in 8 seconds. How fast did it travel?

Board


A toy car travels 40 feet in 8 seconds. How fast did it travel?

change in dis tan ceslope

change in time

traveled 40 feetslope

in 8 seconds

slope 5 ft / sec

Board Answer


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

of hoursCharge of labor

2 160

3 210

4 260

8 460

Board


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

of hoursCharge of labor

2 160

3 210

4 260

8 460

$50

$50

$200

1 hr

1 hr

4 hr

$50/1hr = $50/hr

$50/1hr = $50/hr

$200/4hr = $50/hr

The hourly rate is _____________$50/hr

change in moneyslope hourly ch arg e

change in time

Board Answer

Meaning of the Slope and Intercepts 300The 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 50B 40C 25D 20

Board Answer

Meaning of the Slope and Intercepts 300The 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 50B 40C 25D 20

Board Answer

Meaning of the Slope and Intercepts 300The 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

Minutes

Am

ount

of

wat

er (

m3 )

Board

Meaning of the Slope and Intercepts 300The 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

Minutes

Am

ount

of

wat

er (

m3 )

The water is leaking at _______ m3/min

m hourly ch arg e

change in amt. of water

change in time

3 330m 24m

40min 0min

36m

40min

= 3/20 m3/min

= 0.15 m3/min

0.15

Board Answer

Meaning of the Slope and Intercepts 400The 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

Meaning of the Slope and Intercepts 400The 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 heightm

change in time

1500 ftm

180sec = 8 ft/sec

Board Answer

Meaning of the Slope and Intercepts 500What 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

Meaning of the Slope and Intercepts 500What 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 =

b = 6

B m = 5

b = −2

1

3 C m =

b = −2

D m = 3

b = 6

1

5

x − 3y = 6Solve for y-x -x

-3y = -x + 6-3 -3 -3

y = (1/3)x – 2

Board Answer

Problem Solving 100Mike 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 The speed of the car prior to accelerationB The length of time Mike acceleratedC The speed limitD The rate of acceleration

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 The speed of the car prior to accelerationB The length of time Mike acceleratedC The speed limitD The rate of acceleration

Board

Problem Solving 100

Board Answer

Problem Solving 200Rinaldo’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.

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 200

Board Answer

Problem Solving 300As part of a classroom assignment, Kimberly was given this geoboard to model the slope of 2

3If 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 WG From peg V to peg XH From peg V to peg YJ From peg V to peg Z

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 WG From peg V to peg XH From peg V to peg YJ From peg V to peg Z

Board

Problem Solving 300As part of a classroom assignment, Kimberly was given this geoboard to model the slope of 2

3

2 2

3 3

Board Answer

Problem Solving 400Nikolay 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 = x H y = x

G y = x J y = x

9

25

16

25

9

16

16

9

F y = x H y = x

G y = x J y = x

9

25

16

25

9

16

16

9

Board

Problem Solving 400Nikolay 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

Board Answer

Problem Solving 500The 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.

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

Problem Solving 500

Final Jeopardy Category

Final Jeopardy Category

Board

Final Jeopardy QuestionFinal Jeopardy Question

Answer

What is the y-intercept of the function graphed below?

A −24B −21C −18D −9

Board

Final Jeopardy AnswerFinal Jeopardy Answer

A −24B −21C −18D −9


-14

-4

Slope = _________

14 7

4 2

Board

Final Jeopardy AnswerFinal Jeopardy Answer

A −24B −21C −18D −9


-7

-2

Slope = _________

14 7

4 2

( , )8 10

-7

-2(4, -4)

(2, -11)

One more time ________(0, -18)

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