Question
Which linear graph represents a proportional relationship?
Group of answer choices
a graph of a line that passes through the points 0 comma 0 and 0.5 comma negative 3
a graph of a line that passes through the points 0 comma 2 and 1 comma 5
a graph of a line that passes through the points 0 comma 4 and 1 comma 4
a graph of a line that passes through the points 0 comma negative 0.5 and negative 1 comma 0
Flag question: Question 2
Question 21 pts
M08.B-E.2.1.1
Lesson 1
Which of the following tables represents a linear relationship that is also proportional?
Group of answer choices
x −3 0 3
y 0 2 4
x −4 −2 0
y −2 0 2
x −4 0 4
y 1 0 −1
x −1 0 1
y −5 −3 −1
Flag question: Question 3
Question 31 pts
M08.B-E.2.1.1
Lesson 2
The graph below shows the height through which an elevator travels, y, in x seconds:
A graph is shown with x axis title as Time in seconds. The title on the y-axis is Height of Elevator Above Ground in feet. The values on the x-axis are from 0 to 5 in increments of 1 for each grid line. The values on the y-axis are from 0 to 125 in increments of 25 for each grid line. A line is shown connecting points on ordered pair 1, 25 and 2, 50 and 3, 75 and 4, 100. The title of the graph is Rate of Ascent.
What is the rate of change for the relationship represented in the graph?
Group of answer choices
50
25
fraction 1 over 25
fraction 1 over 50
Flag question: Question 4
Question 41 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes:
A graph is shown. On the x-axis, the values are from 0 till 150 in increments of 30 for each grid line, and on the y-axis, the values are from 0 to 20 in increments of 4 for each grid line. The title of the graph on the x-axis is Time in minutes, and the title on the y-axis is Number of Sprays. A line is shown connecting ordered pairs 30, 4 and 60, 8 and 90, 12 and 120,16. The title for the graph is Dispense Rate.
Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?
Group of answer choices
fraction 4 over 30
fraction 30 over 4
fraction 30 over 16
fraction 16 over 30
Flag question: Question 5
Question 51 pts
M08.B-E.2.1.1
Lesson 2
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
Which statement correctly compares the rates of these representations?
Group of answer choices
The graph has a rate that is greater than the table.
The table has a rate that is greater than the graph.
Flag question: Question 6
Question 61 pts
M08.B-E.2.1.2
Lesson 3
The figure below shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x-axis values are from negative 10 to positive 10 in increments of 2 for each grid line. The y-axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 8, 4, and 0, 0, and 8, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 4, 2 labeled as A, one leg is from 0, 0 to negative 4, 0, and the second leg is from negative 4, 0 to negative 4, 2. Another shaded right triangle is formed with the hypotenuse from negative 4, 2 to negative 6, 3, labeled as B, one leg is from negative 4, 2 to negative 6, 2, and the second leg is between negative 6, 2 to negative 6, 3.
Which statement about the slope of the line is true?
Group of answer choices
It is −2 throughout the line.
It is fraction negative 1 over 2 throughout the line.
The slope from point O to point A is fraction 1 over 2 times the slope of the line from point A to point B.
The slope from point O to point A is two times the slope of the line from point A to point B.
Flag question: Question 7
Question 71 pts
M08.B-E.2.1.3
Lesson 3
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x- and y-axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 5 with the ordered pair 6, 0.
Group of answer choices
0
1
5
6
Flag question: Question 8
Question 81 pts
M08.B-E.2.1.1
Lesson 4
The graph shows the distance y, in miles, of a moving train from a station over a certain period of time, x, in hours:
A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Station in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 40, 80, 120, 160, 200, 240, 280, 320. The graph shows a straight line joining the ordered pairs 0, 80, and 1, 120, and 2, 160, and 3, 200, and 4, 240.
What is the speed (in miles per hour) of the train and why?
Group of answer choices
80 miles per hour, because speed is the initial value of the function
120 miles per hour, because speed is the distance traveled in unit time
240 miles per hour, because speed is the distance traveled in a certain time
40 miles per hour, because speed is the rate of change of distance
Flag question: Question 9
Question 91 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A bakery sells coffee and bagel breakfast packages. The total cost, y, is calculated according to the number of bagels on the platter, x. The gallon container of coffee costs $4.65 and $0.85 is charged for each bagel.
What is the slope of this situation?
Group of answer choices
-4.65
4.65
0.85
-0.85
Flag question: Question 10
Question 101 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A linear relationship is given in the table.
x y
−1 6
0 3
1 0
2 −3
What is the initial value in this linear relationship?
Group of answer choices
−3
0
2
3
Flag question: Question 11
Question 111 pts
M08.B-E.2.1.3
Lesson 4
Sherlock wants to rent a textbook. He has to pay a fixed base cost plus a daily rate for renting the textbook.
The table shows the amount of money, y, in dollars, that Sherlock has to pay for renting the textbook for x days:
Textbook Rental
Number of days
(x) Rent (dollars)
(y)
0 6
1 13
2 20
3 27
4 34
Which equation best shows the relationship between x and y?
Group of answer choices
y = x + 13
y = 7x + 13
y = x + 6
y = 7x + 6
Flag question: Question 12
Question 121 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A Girl Scout is selling cookies to raise money for her troop. She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day. The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.
Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 24 18 15 6
Which of the following graphs shows the relationship given in the table?
Group of answer choices
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 23 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 23
Flag question: Question 13
Question 131 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the price, in dollars, of different numbers of Bannock Burgers at Hugo's store. The table shows the price, in dollars, of different numbers of popovers at the same store.
A graph shows Number of Bannock burgers on x-axis and Price of Bannock burgers on y-axis. The x-axis scale is shown from 0 to 18 at increments of 3, and the y-axis scale is shown from 0 to 240 at increments of 30. A straight line joins the ordered pairs 3, 30 and 6, 60 and 9, 90 and 12, 120 and 15, 150 and 18, 180.
Popovers
Number
of Popovers Price of Popovers
(dollars)
3 12
6 24
9 36
12 48
How much more does it cost to get a Bannock Burger than a popover at Hugo's?
Group of answer choices
$3
$4
$6
$10
one sentence answer for each please
Group of answer choices
a graph of a line that passes through the points 0 comma 0 and 0.5 comma negative 3
a graph of a line that passes through the points 0 comma 2 and 1 comma 5
a graph of a line that passes through the points 0 comma 4 and 1 comma 4
a graph of a line that passes through the points 0 comma negative 0.5 and negative 1 comma 0
Flag question: Question 2
Question 21 pts
M08.B-E.2.1.1
Lesson 1
Which of the following tables represents a linear relationship that is also proportional?
Group of answer choices
x −3 0 3
y 0 2 4
x −4 −2 0
y −2 0 2
x −4 0 4
y 1 0 −1
x −1 0 1
y −5 −3 −1
Flag question: Question 3
Question 31 pts
M08.B-E.2.1.1
Lesson 2
The graph below shows the height through which an elevator travels, y, in x seconds:
A graph is shown with x axis title as Time in seconds. The title on the y-axis is Height of Elevator Above Ground in feet. The values on the x-axis are from 0 to 5 in increments of 1 for each grid line. The values on the y-axis are from 0 to 125 in increments of 25 for each grid line. A line is shown connecting points on ordered pair 1, 25 and 2, 50 and 3, 75 and 4, 100. The title of the graph is Rate of Ascent.
What is the rate of change for the relationship represented in the graph?
Group of answer choices
50
25
fraction 1 over 25
fraction 1 over 50
Flag question: Question 4
Question 41 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes:
A graph is shown. On the x-axis, the values are from 0 till 150 in increments of 30 for each grid line, and on the y-axis, the values are from 0 to 20 in increments of 4 for each grid line. The title of the graph on the x-axis is Time in minutes, and the title on the y-axis is Number of Sprays. A line is shown connecting ordered pairs 30, 4 and 60, 8 and 90, 12 and 120,16. The title for the graph is Dispense Rate.
Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?
Group of answer choices
fraction 4 over 30
fraction 30 over 4
fraction 30 over 16
fraction 16 over 30
Flag question: Question 5
Question 51 pts
M08.B-E.2.1.1
Lesson 2
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
Which statement correctly compares the rates of these representations?
Group of answer choices
The graph has a rate that is greater than the table.
The table has a rate that is greater than the graph.
Flag question: Question 6
Question 61 pts
M08.B-E.2.1.2
Lesson 3
The figure below shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x-axis values are from negative 10 to positive 10 in increments of 2 for each grid line. The y-axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 8, 4, and 0, 0, and 8, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 4, 2 labeled as A, one leg is from 0, 0 to negative 4, 0, and the second leg is from negative 4, 0 to negative 4, 2. Another shaded right triangle is formed with the hypotenuse from negative 4, 2 to negative 6, 3, labeled as B, one leg is from negative 4, 2 to negative 6, 2, and the second leg is between negative 6, 2 to negative 6, 3.
Which statement about the slope of the line is true?
Group of answer choices
It is −2 throughout the line.
It is fraction negative 1 over 2 throughout the line.
The slope from point O to point A is fraction 1 over 2 times the slope of the line from point A to point B.
The slope from point O to point A is two times the slope of the line from point A to point B.
Flag question: Question 7
Question 71 pts
M08.B-E.2.1.3
Lesson 3
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x- and y-axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 5 with the ordered pair 6, 0.
Group of answer choices
0
1
5
6
Flag question: Question 8
Question 81 pts
M08.B-E.2.1.1
Lesson 4
The graph shows the distance y, in miles, of a moving train from a station over a certain period of time, x, in hours:
A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Station in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 40, 80, 120, 160, 200, 240, 280, 320. The graph shows a straight line joining the ordered pairs 0, 80, and 1, 120, and 2, 160, and 3, 200, and 4, 240.
What is the speed (in miles per hour) of the train and why?
Group of answer choices
80 miles per hour, because speed is the initial value of the function
120 miles per hour, because speed is the distance traveled in unit time
240 miles per hour, because speed is the distance traveled in a certain time
40 miles per hour, because speed is the rate of change of distance
Flag question: Question 9
Question 91 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A bakery sells coffee and bagel breakfast packages. The total cost, y, is calculated according to the number of bagels on the platter, x. The gallon container of coffee costs $4.65 and $0.85 is charged for each bagel.
What is the slope of this situation?
Group of answer choices
-4.65
4.65
0.85
-0.85
Flag question: Question 10
Question 101 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A linear relationship is given in the table.
x y
−1 6
0 3
1 0
2 −3
What is the initial value in this linear relationship?
Group of answer choices
−3
0
2
3
Flag question: Question 11
Question 111 pts
M08.B-E.2.1.3
Lesson 4
Sherlock wants to rent a textbook. He has to pay a fixed base cost plus a daily rate for renting the textbook.
The table shows the amount of money, y, in dollars, that Sherlock has to pay for renting the textbook for x days:
Textbook Rental
Number of days
(x) Rent (dollars)
(y)
0 6
1 13
2 20
3 27
4 34
Which equation best shows the relationship between x and y?
Group of answer choices
y = x + 13
y = 7x + 13
y = x + 6
y = 7x + 6
Flag question: Question 12
Question 121 pts
M08.B-E.2.1.3, M08.B-F.2.1.1
Lesson 4
A Girl Scout is selling cookies to raise money for her troop. She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day. The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.
Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 24 18 15 6
Which of the following graphs shows the relationship given in the table?
Group of answer choices
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 21
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 23 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 19
a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 27 and 2 comma 23
Flag question: Question 13
Question 131 pts
M08.B-E.2.1.1
Lesson 2
The graph shows the price, in dollars, of different numbers of Bannock Burgers at Hugo's store. The table shows the price, in dollars, of different numbers of popovers at the same store.
A graph shows Number of Bannock burgers on x-axis and Price of Bannock burgers on y-axis. The x-axis scale is shown from 0 to 18 at increments of 3, and the y-axis scale is shown from 0 to 240 at increments of 30. A straight line joins the ordered pairs 3, 30 and 6, 60 and 9, 90 and 12, 120 and 15, 150 and 18, 180.
Popovers
Number
of Popovers Price of Popovers
(dollars)
3 12
6 24
9 36
12 48
How much more does it cost to get a Bannock Burger than a popover at Hugo's?
Group of answer choices
$3
$4
$6
$10
one sentence answer for each please
Answers
GPT-4o mini
Sure! Here are the answers for each question, providing a concise sentence for each:
1. **Question 1**: The graph of a line that passes through the points 0, 0 and 0.5, -3 represents a proportional relationship because it includes the origin (0,0).
2. **Question 2**: The table with x = -4, -2, 0 and y = -2, 0, 2 represents a linear relationship that is also proportional because it passes through the origin.
3. **Question 3**: The rate of change for the relationship represented in the graph is 25, as it increases 25 feet for each second.
4. **Question 4**: The expression that can be used to calculate the rate per minute at which the air freshener dispenses sprays is 4 over 30, indicating 4 sprays in 30 minutes.
5. **Question 5**: The table has a rate that is greater than the graph because the y-values in the graph do not increase as quickly as in the table.
6. **Question 6**: The slope from point O to point A is fraction negative 1 over 2 throughout the line, indicating consistent negative slope.
7. **Question 7**: The initial value of the function represented by this graph is 5, which is the y-intercept when x = 0.
8. **Question 8**: The speed of the train is 40 miles per hour, because speed is defined as the rate of change of distance with respect to time.
9. **Question 9**: The slope of this situation is 0.85, representing the cost per bagel added to the fixed cost of coffee.
10. **Question 10**: The initial value in this linear relationship is 3, which corresponds to the value of y when x = 0.
11. **Question 11**: The equation that best shows the relationship between x and y is y = 7x + 6, indicating a base cost with a daily rental rate.
12. **Question 12**: The correct graph is the one that passes through the points 0, 27 and 2, 23, reflecting the remaining boxes over time.
13. **Question 13**: It costs $6 more to get a Bannock Burger than a popover at Hugo's, as calculated from the prices per quantity.
1. **Question 1**: The graph of a line that passes through the points 0, 0 and 0.5, -3 represents a proportional relationship because it includes the origin (0,0).
2. **Question 2**: The table with x = -4, -2, 0 and y = -2, 0, 2 represents a linear relationship that is also proportional because it passes through the origin.
3. **Question 3**: The rate of change for the relationship represented in the graph is 25, as it increases 25 feet for each second.
4. **Question 4**: The expression that can be used to calculate the rate per minute at which the air freshener dispenses sprays is 4 over 30, indicating 4 sprays in 30 minutes.
5. **Question 5**: The table has a rate that is greater than the graph because the y-values in the graph do not increase as quickly as in the table.
6. **Question 6**: The slope from point O to point A is fraction negative 1 over 2 throughout the line, indicating consistent negative slope.
7. **Question 7**: The initial value of the function represented by this graph is 5, which is the y-intercept when x = 0.
8. **Question 8**: The speed of the train is 40 miles per hour, because speed is defined as the rate of change of distance with respect to time.
9. **Question 9**: The slope of this situation is 0.85, representing the cost per bagel added to the fixed cost of coffee.
10. **Question 10**: The initial value in this linear relationship is 3, which corresponds to the value of y when x = 0.
11. **Question 11**: The equation that best shows the relationship between x and y is y = 7x + 6, indicating a base cost with a daily rental rate.
12. **Question 12**: The correct graph is the one that passes through the points 0, 27 and 2, 23, reflecting the remaining boxes over time.
13. **Question 13**: It costs $6 more to get a Bannock Burger than a popover at Hugo's, as calculated from the prices per quantity.