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Finding Intercepts Changing Slopes and y-intercepts Meaning of the Slope and Intercepts Problem Solving Final Jeopardy Jeopardy Board

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

Board Finding Intercepts 100 What 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

BoardAnswer Finding Intercepts 200 Which 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

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

Board Finding Intercepts 300 What is the y-intercept of the function f (x) = 3(x − 2)? F 3 G 1 H −2 J −6 y = mx + b f (x) = 3(x − 2) m = __________ slope b = __________ y-intercept Simplify f (x) = 3x − 6

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

Board Finding Intercepts 400 A (0, 2) B (0, ) C(0, 5) D (0, 10) y = mx + b 4x + 2y = 10 m = __________ slope b = __________ y-intercept Solve for y -4x 2y = -4x y = -2x + 5

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

Board Finding Intercepts 500 What are the coordinates of the x-intercept of the equation −3y = 8 − 2x? F (−2, 0) G (0, − ) H (, 0) J(4, 0) Solve for y -3y = 8 – 2x -3 Check: (x, y) -3y = 8 – 2x -3(0) = 8 – 2(4)

BoardAnswer 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 Changing Slopes and y-intercepts 100 y = 4x + 8 y = 4x – 3 4x + 84x – 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. 44 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. HThe slope will increase. J The slope will decrease. BoardAnswer Changing Slopes and y-intercepts 200

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. HThe slope will increase. J The slope will decrease.

BoardAnswer 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? AThe 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 300 Given the function y = 3.54x − 54.68, which statement best describes the effect of increasing the y-intercept by 33.14? AThe 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 the effect on the graph when the slope is doubled? A The y-intercept increases. B The y-intercept decreases. CThe x-intercept increases. D The x-intercept decreases. BoardAnswer Changing Slopes and y-intercepts 400

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. CThe x-intercept increases. D The x-intercept decreases. y = mx + b m = __________ slope b = __________ y-intercept y = __x m = __________ 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? Ay = −2x + 1 B y = −x + 1 C y = −x − 1 D y = − x − 1 BoardAnswer Changing Slopes and y-intercepts 500

Board 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? Ay = −2x + 1 B y = −x + 1 C y = −x − 1 D y = − x − 1 y = mx + b m = __________ slope b = __________ y-intercept b = _______ m = _______ 3  -1 = -2 – 2 = 1 y = -2x + 1

BoardAnswer Meaning of the Slope and Intercepts 100 A toy car travels 40 feet in 8 seconds. How fast did it travel?

Board Meaning of the Slope and Intercepts 100 A toy car travels 40 feet in 8 seconds. How fast did it travel?

BoardAnswer 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 of hours Charge of labor

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 of hours Charge of labor $50 $200 1 hr 4 hr $50/1hr = $50/hr $200/4hr = $50/hr The hourly rate is _____________ $50/hr

BoardAnswer 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 50 B 40 C 25 D20

BoardAnswer 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 50 B 40 C 25 D20

BoardAnswer 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 m 3 per min Minutes Amount of water (m 3 )

Board 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 m 3 per min Minutes Amount of water (m 3 ) The water is leaking at _______ m 3 /min = 3/20 m 3 /min = 0.15 m 3 /min 0.15

BoardAnswer 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. GThe 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 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. GThe 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. = 8 ft/sec

BoardAnswer 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 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 = b = 6 B m = 5 b = −2 Cm = b = −2 D m = 3 b = 6 x − 3y = 6 Solve for y -x -3y = -x y = (1/3)x – 2

BoardAnswer 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 The speed of the car prior to acceleration B The length of time Mike accelerated C The speed limit DThe 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 acceleration B The length of time Mike accelerated C The speed limit DThe rate of acceleration Board Problem Solving 100

BoardAnswer 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.

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

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

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

BoardAnswer 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 = xH y = x Gy = xJ y = x

F y = xH y = x Gy = xJ y = x Board 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

BoardAnswer Problem Solving 500 The function g(x) = (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. CThe 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) = (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. CThe 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 Board

Final Jeopardy Question Answer What is the y-intercept of the function graphed below? A −24 B −21 C−18 D −9

Board Final Jeopardy Answer A −24 B −21 C−18 D −9 What is the y-intercept of the function graphed below? Slope = _________

Board Final Jeopardy Answer A −24 B −21 C−18 D −9 What is the y-intercept of the function graphed below? Slope = _________ (, ) (4, -4) (2, -11) One more time ________ (0, -18)