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
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.
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).
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 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.
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.
To answer this question, let's analyze the given points:
(0, 600) represents the number of weeks (x-axis) and the amount of money (y-axis). In the first week, Stacy paid $600 to her parents.
(4, 400) indicates that after 4 weeks, Stacy's payment decreased to $400.
(8, 200) shows that after 8 weeks, Stacy paid only $200.
Finally, (12, 0) suggests that by the end of 12 weeks, Stacy stopped paying any money to her parents.
From this information, we observe a pattern of weekly payments decreasing by $200 every 4 weeks. So, Stacy's payment reduced by $200 every 4 weeks.
Therefore, to determine how much money per week Stacy paid to her parents, we need to calculate the decrease in payment per week.
First, let's calculate the total decrease in payment over the 12 weeks:
Total decrease = (Total number of 4-week cycles) × (Decrease per cycle)
Total decrease = (12 ÷ 4) × $200 = 3 × $200 = $600
Now, we can find how much money Stacy paid per week by subtracting the total decrease from the initial payment:
Initial payment - Total decrease = $600 - $600 = $0
Based on these calculations, Stacy did not pay any money per week to her parents after the initial payment of $600. Therefore, the correct answer is $0, and none of the given options [$50, $200, $100, $25] are applicable.