Question
he following points fare graphed (0, 600), (4, 400), (8, 200) and (12, 0).
How much money per week did Stacy pay to her parents?
$50
$200
$100
$25
How much money per week did Stacy pay to her parents?
$50
$200
$100
$25
Answers
Answer
What is the constant rate of change for the graph below?
Graph. The x-axis has a range of 0 to 6 with intervals of 2. The y-axis has a range of 0 to 20 with intervals of 5. The line increases from left to right and has points at (0,0), (2,6), (4, 12) and (6,18).
Note: In case it is hard to see there are points at (0,0), (2, 6), (4, 12), and (6, 18).
Graph. The x-axis has a range of 0 to 6 with intervals of 2. The y-axis has a range of 0 to 20 with intervals of 5. The line increases from left to right and has points at (0,0), (2,6), (4, 12) and (6,18).
Note: In case it is hard to see there are points at (0,0), (2, 6), (4, 12), and (6, 18).
Answer
the following points are graphed (0,0), (4, 6), (8, 12), (12, 18).
Which of the statements is supported by the rate of change in this situation?
The graph below represents the relationship between the number of pages Jacob has read and the number of minutes he has been reading.
Graph is titled Jacob Reading a Book. The x-axis is titled Number of Pages Read and has a range of 0 to 12 with intervals of 2. The y-axis is titled Time (minutes) and has a range of 0 to 20 with intervals of 5. A line is increasing from left to right and starts at the origin and ends at (12,18). Other points on the line are (4, 6) and (8, 12).
Note: In case it is hard to see, the following points are graphed (0,0), (4, 6), (8, 12), (12, 18).
Which of the statements is supported by the rate of change in this situation?
Jacob is reading 3 pages in 2 minutes.
Jacob is reading 8 pages in 10 minutes.
Jacob is reading 9 pages in 6 minutes.
Jacob is reading 1 page in 1.5 minutes.
Which of the statements is supported by the rate of change in this situation?
The graph below represents the relationship between the number of pages Jacob has read and the number of minutes he has been reading.
Graph is titled Jacob Reading a Book. The x-axis is titled Number of Pages Read and has a range of 0 to 12 with intervals of 2. The y-axis is titled Time (minutes) and has a range of 0 to 20 with intervals of 5. A line is increasing from left to right and starts at the origin and ends at (12,18). Other points on the line are (4, 6) and (8, 12).
Note: In case it is hard to see, the following points are graphed (0,0), (4, 6), (8, 12), (12, 18).
Which of the statements is supported by the rate of change in this situation?
Jacob is reading 3 pages in 2 minutes.
Jacob is reading 8 pages in 10 minutes.
Jacob is reading 9 pages in 6 minutes.
Jacob is reading 1 page in 1.5 minutes.
Answered by
GPT 3.5
To determine how much money Stacy paid to her parents per week, we need to calculate the slope of the line connecting the points (0, 600) and (4, 400).
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 600) and (4, 400):
m = (400 - 600) / (4 - 0)
= -200 / 4
= -50
Since the slope is -50, this means that for every 1 unit increase in the x-coordinate (weeks), there is a decrease of $50 in the y-coordinate (money paid to parents).
To find out how much Stacy paid per week, we can use the slope-intercept form of a line:
y = mx + b
Plugging in the slope and the coordinates of one of the points (e.g., (0, 600)), we can solve for b:
600 = -50(0) + b
b = 600
Therefore, the equation of the line is:
y = -50x + 600
To find out how much money Stacy paid per week, we can plug in the x-coordinate of any point and solve for y. Let's use x = 8:
y = -50(8) + 600
y = -400 + 600
y = 200
Therefore, Stacy paid $200 per week to her parents.
The correct answer is $200.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 600) and (4, 400):
m = (400 - 600) / (4 - 0)
= -200 / 4
= -50
Since the slope is -50, this means that for every 1 unit increase in the x-coordinate (weeks), there is a decrease of $50 in the y-coordinate (money paid to parents).
To find out how much Stacy paid per week, we can use the slope-intercept form of a line:
y = mx + b
Plugging in the slope and the coordinates of one of the points (e.g., (0, 600)), we can solve for b:
600 = -50(0) + b
b = 600
Therefore, the equation of the line is:
y = -50x + 600
To find out how much money Stacy paid per week, we can plug in the x-coordinate of any point and solve for y. Let's use x = 8:
y = -50(8) + 600
y = -400 + 600
y = 200
Therefore, Stacy paid $200 per week to her parents.
The correct answer is $200.
Answered by
GPT 3.5
The constant rate of change is the same as the slope of the line connecting any two points on the graph. Let's calculate the slope using the points (0,0) and (2,6).
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,0) and (2,6):
m = (6 - 0) / (2 - 0)
= 6 / 2
= 3
Therefore, the constant rate of change for the graph is 3.
Note: The constant rate of change represents how much the y-coordinate increases for every 1 unit increase in the x-coordinate. In this case, for every 1 unit increase in x, the y-coordinate increases by 3.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,0) and (2,6):
m = (6 - 0) / (2 - 0)
= 6 / 2
= 3
Therefore, the constant rate of change for the graph is 3.
Note: The constant rate of change represents how much the y-coordinate increases for every 1 unit increase in the x-coordinate. In this case, for every 1 unit increase in x, the y-coordinate increases by 3.
Answered by
GPT 3.5
To determine the rate of change in this situation, we need to calculate the slope of the line connecting the points (0,0) and (12,18).
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,0) and (12,18):
m = (18 - 0) / (12 - 0)
= 18 / 12
= 1.5
Therefore, the rate of change for Jacob in this situation is 1.5. This means that for every 1 unit increase in the x-coordinate (number of pages read), there is an increase of 1.5 in the y-coordinate (time in minutes).
Based on this rate of change, the statement "Jacob is reading 1 page in 1.5 minutes" is supported by the graph and rate of change.
Therefore, Jacob is reading 1 page in 1.5 minutes.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,0) and (12,18):
m = (18 - 0) / (12 - 0)
= 18 / 12
= 1.5
Therefore, the rate of change for Jacob in this situation is 1.5. This means that for every 1 unit increase in the x-coordinate (number of pages read), there is an increase of 1.5 in the y-coordinate (time in minutes).
Based on this rate of change, the statement "Jacob is reading 1 page in 1.5 minutes" is supported by the graph and rate of change.
Therefore, Jacob is reading 1 page in 1.5 minutes.