Question
What is the rate of change of the linear relationship modeled in the table? (4 points)
x y
−2 5
−1 4
0 3
1 2
−2
−1
negative one over two
1
x y
−2 5
−1 4
0 3
1 2
−2
−1
negative one over two
1
Answers
Answer
Based on the graph, what is the initial value of the linear relationship? (4 points)
A coordinate plane is shown. A line passes through the y-axis at -2 and the x-axis at 3.
−2
0
two over three
3
A coordinate plane is shown. A line passes through the y-axis at -2 and the x-axis at 3.
−2
0
two over three
3
Answer
Which scenario best matches the linear relationship expressed in the equation y = 32x + 80? (4 points)
Joseph has $80 in his bank account and spends $32 each day.
Joseph has $80 in his bank account and earns $32 each day.
Joseph had $32 in his bank account and deposited another $80.
Joseph has $32 in his bank account and earns $80 each day.
Joseph has $80 in his bank account and spends $32 each day.
Joseph has $80 in his bank account and earns $32 each day.
Joseph had $32 in his bank account and deposited another $80.
Joseph has $32 in his bank account and earns $80 each day.
Answer
Which scenario best matches the linear relationship shown in the table? (4 points)
Days Dollars
0 76
2 48
4 20
6 −8
Kathryn had $76 and spent $28 each day.
Kathryn had $76 and earns $14 per day.
Kathryn had $76 and spent $14 each day.
Kathryn spends $28 each day.
Days Dollars
0 76
2 48
4 20
6 −8
Kathryn had $76 and spent $28 each day.
Kathryn had $76 and earns $14 per day.
Kathryn had $76 and spent $14 each day.
Kathryn spends $28 each day.
Answer
Seth and Jennifer are trying to figure out how long they can live off their $22,500 savings if they spend $530 each month. They have each created an equation.
Seth's Equation Jennifer's Equation
y = 22,500 + (530x) y = 22,500 − (530x)
Which person has the correct equation to model this linear relationship? (4 points)
Jennifer's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
Jennifer's equation is incorrect, because their spending will increase the amount of their savings.
Seth's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
Seth's equation is incorrect, because their spending should be a fixed amount and should not be multiplied.
Seth's Equation Jennifer's Equation
y = 22,500 + (530x) y = 22,500 − (530x)
Which person has the correct equation to model this linear relationship? (4 points)
Jennifer's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
Jennifer's equation is incorrect, because their spending will increase the amount of their savings.
Seth's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
Seth's equation is incorrect, because their spending should be a fixed amount and should not be multiplied.
Answered by
GPT 3.5
To find the rate of change, we can calculate the difference in y-values for any two x-values.
For example, if we compare the y-values for x = -2 and x = -1, the difference is 4 - 5 = -1.
Similarly, the difference in y-values for x = -1 and x = 0 is 3 - 4 = -1, and for x = 0 and x = 1 is 2 - 3 = -1.
Since the difference in y-values is constant for any two x-values, the rate of change of this linear relationship is -1.
Therefore, the correct answer is -1.
For example, if we compare the y-values for x = -2 and x = -1, the difference is 4 - 5 = -1.
Similarly, the difference in y-values for x = -1 and x = 0 is 3 - 4 = -1, and for x = 0 and x = 1 is 2 - 3 = -1.
Since the difference in y-values is constant for any two x-values, the rate of change of this linear relationship is -1.
Therefore, the correct answer is -1.
Answered by
GPT 3.5
The initial value of a linear relationship is the value of y when x is equal to 0.
In this case, the line passes through the x-axis at 3, so when x is 0, the y-value is 3.
Therefore, the initial value of the linear relationship is 3.
Thus, the correct answer is 3.
In this case, the line passes through the x-axis at 3, so when x is 0, the y-value is 3.
Therefore, the initial value of the linear relationship is 3.
Thus, the correct answer is 3.
Answered by
GPT 3.5
The equation y = 32x + 80 represents a linear relationship where the y-value represents the total amount of money and the x-value represents the number of days.
From the equation, we can see that the initial value (y-intercept) is 80, indicating that Joseph starts with $80 in his bank account.
The coefficient of x is 32, indicating that for each day, Joseph adds $32 to his account.
Therefore, the scenario that best matches the linear relationship expressed by the equation y = 32x + 80 is:
Joseph had $32 in his bank account and deposited another $80.
Thus, the correct answer is "Joseph had $32 in his bank account and deposited another $80."
From the equation, we can see that the initial value (y-intercept) is 80, indicating that Joseph starts with $80 in his bank account.
The coefficient of x is 32, indicating that for each day, Joseph adds $32 to his account.
Therefore, the scenario that best matches the linear relationship expressed by the equation y = 32x + 80 is:
Joseph had $32 in his bank account and deposited another $80.
Thus, the correct answer is "Joseph had $32 in his bank account and deposited another $80."
Answered by
GPT 3.5
To determine which scenario best matches the linear relationship shown in the table, we need to analyze the rate of change.
From the table, we can observe that for every 2 days that pass, the total number of dollars decreases by 28. This means that for each interval of 2 days, $28 is being spent.
Therefore, the scenario that best matches the linear relationship shown in the table is:
Kathryn had $76 and spent $14 each day.
Thus, the correct answer is "Kathryn had $76 and spent $14 each day."
From the table, we can observe that for every 2 days that pass, the total number of dollars decreases by 28. This means that for each interval of 2 days, $28 is being spent.
Therefore, the scenario that best matches the linear relationship shown in the table is:
Kathryn had $76 and spent $14 each day.
Thus, the correct answer is "Kathryn had $76 and spent $14 each day."
Answered by
GPT 3.5
To determine which person has the correct equation to model the given linear relationship, we need to analyze the relationship between their savings and spending.
The equation y = 22,500 + (530x) suggests that the savings y will increase as x (the number of months) increases, because the spending is being added to the initial savings of $22,500.
On the other hand, the equation y = 22,500 - (530x) suggests that the savings y will decrease as x (the number of months) increases, because the spending is being subtracted from the initial savings of $22,500.
Since Seth and Jennifer are trying to figure out how long they can live off their savings, it makes sense that their savings will gradually decrease as they spend money each month. Therefore, the correct equation to model this linear relationship is:
Jennifer's equation is incorrect, because their spending will increase the amount of their savings.
Seth's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
Thus, the correct answer is "Seth's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings."
The equation y = 22,500 + (530x) suggests that the savings y will increase as x (the number of months) increases, because the spending is being added to the initial savings of $22,500.
On the other hand, the equation y = 22,500 - (530x) suggests that the savings y will decrease as x (the number of months) increases, because the spending is being subtracted from the initial savings of $22,500.
Since Seth and Jennifer are trying to figure out how long they can live off their savings, it makes sense that their savings will gradually decrease as they spend money each month. Therefore, the correct equation to model this linear relationship is:
Jennifer's equation is incorrect, because their spending will increase the amount of their savings.
Seth's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
Thus, the correct answer is "Seth's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings."
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