To transform the equation \( y = \frac{2}{3}x - 4 \) to \( y = \frac{2}{3}x \), we need to eliminate the \(-4\) from the equation. This can be done by shifting the graph up 4 units.
Therefore, the correct response is:
Shift the graph up 4.
The equation of this graph is y = 2/3 x − 4
What transformation would need to happen for the equation of the line to be y = 2/3 x?
(1 point)
Responses
Shift the graph up 4
Shift the graph up 4
Shift the graph right 3, down 2
Shift the graph right 3, down 2
Shift the graph down 3 and left 2
Shift the graph down 3 and left 2
Shift the graph left 4
11 answers
A cab company charges $8 per mile for a lift to the airport.
What change would the company make to their charges to make this a non proportional situation?
(1 point)
Responses
Charge a flat rate of $10 and then $8 per mile
Charge a flat rate of $10 and then $8 per mile
No changes are needed
No changes are needed
Charge $12 per mile instead of $8
Charge $12 per mile instead of $8
Charge $4 per mile instead of $8
Charge $4 per mile instead of $8
Question 6
What change would the company make to their charges to make this a non proportional situation?
(1 point)
Responses
Charge a flat rate of $10 and then $8 per mile
Charge a flat rate of $10 and then $8 per mile
No changes are needed
No changes are needed
Charge $12 per mile instead of $8
Charge $12 per mile instead of $8
Charge $4 per mile instead of $8
Charge $4 per mile instead of $8
Question 6
To make the pricing structure non-proportional, the cab company can introduce a flat rate or a fixed charge in addition to the per mile charge.
The option that introduces a flat rate in addition to a per mile charge is:
Charge a flat rate of $10 and then $8 per mile.
This structure is non-proportional because it includes a fixed cost regardless of the distance traveled (the $10 flat rate).
One business charges $12 per t-shirt custom made.
Another business charges $11 per t-shirt plus a $20 set up fee for custom made.
If you were to graph both of these scenarios on the coordinate plane, the first graph would be proportional and the second non proportional.
How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph?
(1 point)
Responses
Right 1
Right 1
Up 1
Up 1
Up 20
Up 20
Left 1
Left 1
Left 20
Left 20
Right 20
Another business charges $11 per t-shirt plus a $20 set up fee for custom made.
If you were to graph both of these scenarios on the coordinate plane, the first graph would be proportional and the second non proportional.
How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph?
(1 point)
Responses
Right 1
Right 1
Up 1
Up 1
Up 20
Up 20
Left 1
Left 1
Left 20
Left 20
Right 20
To transform the first graph (which represents the situation of charging $12 per t-shirt, a proportional relationship, with no fixed cost) into a non-proportional graph like the second one (which charges $11 per t-shirt plus a $20 setup fee), we need to introduce a fixed cost.
The fixed cost in the second scenario is $20, while the y-intercept of the first graph is currently at 0 since there is no fixed fee.
To adjust the first graph so that it has the same y-intercept as the second graph, you would need to shift the graph up by $20. This will incorporate the fixed cost while keeping the linear relationship of $12 per t-shirt.
Thus, the correct response is:
Up 20.
The tables below show the number of jumping jacks completed after a given period of time in minutes.
Kimberly
Time (min) # Jumping Jacks
3 28
8 58
12 82
16 106
Katrina
Time (min) # Jumping Jacks
2 16
5 40
12 96
20 160
(3 points)
The person doing the most jumping jacks per minute
The person that did the most jumping jacks initially before the time started
The person showing a proportional relationship between time and # of jumping jacks
responses
Katrina
Kimberly
neither
both
Kimberly
Time (min) # Jumping Jacks
3 28
8 58
12 82
16 106
Katrina
Time (min) # Jumping Jacks
2 16
5 40
12 96
20 160
(3 points)
The person doing the most jumping jacks per minute
The person that did the most jumping jacks initially before the time started
The person showing a proportional relationship between time and # of jumping jacks
responses
Katrina
Kimberly
neither
both
To analyze the two individuals' performances based on the tables provided:
-
The person doing the most jumping jacks per minute:
-
Calculate the jumping jacks per minute for both:
-
Kimberly:
- \( \frac{28 \text{ jacks}}{3 \text{ minutes}} \approx 9.33 \text{ jacks/min} \)
- \( \frac{58 \text{ jacks}}{8 \text{ minutes}} = 7.25 \text{ jacks/min} \)
- \( \frac{82 \text{ jacks}}{12 \text{ minutes}} \approx 6.83 \text{ jacks/min} \)
- \( \frac{106 \text{ jacks}}{16 \text{ minutes}} = 6.625 \text{ jacks/min} \)
-
Katrina:
- \( \frac{16 \text{ jacks}}{2 \text{ minutes}} = 8 \text{ jacks/min} \)
- \( \frac{40 \text{ jacks}}{5 \text{ minutes}} = 8 \text{ jacks/min} \)
- \( \frac{96 \text{ jacks}}{12 \text{ minutes}} = 8 \text{ jacks/min} \)
- \( \frac{160 \text{ jacks}}{20 \text{ minutes}} = 8 \text{ jacks/min} \)
-
Kimberly has the highest rate of approximately 9.33 jacks/min. Therefore, the answer is Kimberly.
-
-
The person that did the most jumping jacks initially before the time started:
- Both started with 0 jumping jacks before their respective times began, meaning neither did any jumping jacks initially. Therefore, this response would be neither.
-
The person showing a proportional relationship between time and # of jumping jacks:
-
A proportional relationship means that the ratio of jumping jacks to time remains constant.
-
Kimberly: Jumping jacks per minute is not consistent.
-
Katrina:
- Per minute, Katrina maintains a consistent 8 jumping jacks/min.
Therefore, Katrina shows a proportional relationship. The answer is Katrina.
-
Summary of responses:
- The person doing the most jumping jacks per minute: Kimberly
- The person that did the most jumping jacks initially before the time started: neither
- The person showing a proportional relationship between time and # of jumping jacks: Katrina
Function B:
x y
0 1
4 9
8 17
Function C: y=x+20
(4 points)
Function with the greatest rate of change
Function with the smallest y-intercept
Which function would benefit you the most if it represented your money earned per hour?
Function with the highest initial amount of money
responses
function A
function B
function C
x y
0 1
4 9
8 17
Function C: y=x+20
(4 points)
Function with the greatest rate of change
Function with the smallest y-intercept
Which function would benefit you the most if it represented your money earned per hour?
Function with the highest initial amount of money
responses
function A
function B
function C
From the given data, we can analyze Function B and Function C. Let's take a closer look at each of the aspects mentioned in your questions.
Function B:
-
Given points:
- At \(x = 0\), \(y = 1\)
- At \(x = 4\), \(y = 9\)
- At \(x = 8\), \(y = 17\)
-
To find the rate of change (slope) for Function B:
- Between \( (0, 1) \) and \( (4, 9) \): \[ \text{Rate of change} = \frac{9 - 1}{4 - 0} = \frac{8}{4} = 2 \]
- Between \( (4, 9) \) and \( (8, 17) \): \[ \text{Rate of change} = \frac{17 - 9}{8 - 4} = \frac{8}{4} = 2 \]
The rate of change for Function B is consistently \(2\).
Function C:
- Given by the equation \(y = x + 20\):
- The slope (rate of change) is \(1\) (as the coefficient of \(x\) is 1).
- The y-intercept (when \(x = 0\)) is \(20\).
Analysis:
-
Function with the greatest rate of change:
- Function B: Rate of change = 2
- Function C: Rate of change = 1
- Response: Function B
-
Function with the smallest y-intercept:
- Function B: y-intercept = 1 (at \(x = 0\))
- Function C: y-intercept = 20 (at \(x = 0\))
- Response: Function B
-
Which function would benefit you the most if it represented your money earned per hour:
- Function B: Earnings increase by 2 for every hour worked.
- Function C: Earnings increase by 1 for every hour worked, starting from a higher base of 20.
- Since Function B increases at a higher rate, Response: Function B.
-
Function with the highest initial amount of money:
- Function B: Initial amount is 1 (when \(x = 0\)).
- Function C: Initial amount is 20 (when \(x = 0\)).
- Response: Function C.
Summary of Responses:
- Function with the greatest rate of change: Function B
- Function with the smallest y-intercept: Function B
- Which function would benefit you the most if it represented your money earned per hour: Function B
- Function with the highest initial amount of money: Function C
Change the equation from standard form to slope-intercept form by solving for y.
11x−8y=−48
Bob's work:
−8y=−59x
y=7.375
Bill's work:
−8y=−11x−48
y=118x+6
Bud's work:
−8y=−11x−48
y=−11x+6
Who solved for y correctly?
(1 point)
Responses
None of them are correct
None of them are correct
Bob
Bob
Bud
Bud
Bill
11x−8y=−48
Bob's work:
−8y=−59x
y=7.375
Bill's work:
−8y=−11x−48
y=118x+6
Bud's work:
−8y=−11x−48
y=−11x+6
Who solved for y correctly?
(1 point)
Responses
None of them are correct
None of them are correct
Bob
Bob
Bud
Bud
Bill
To determine who solved for \( y \) correctly in the equation \( 11x - 8y = -48 \), we need to solve this equation step-by-step in the correct way and then compare it to the work of Bob, Bill, and Bud.
Starting with the equation:
-
Isolate \( -8y \): \[ 11x - 8y = -48 \] Rearranging gives us: \[ -8y = -11x - 48 \]
-
Divide by \(-8\) to solve for \( y \): \[ y = \frac{-11x - 48}{-8} \] This simplifies to: \[ y = \frac{11}{8}x + 6 \] (since \(-48 / -8 = 6\))
Now, let's analyze Bob's, Bill's, and Bud's work:
-
Bob's work:
- \(-8y = -59x\) → Incorrect.
-
Bill's work:
- \(-8y = -11x - 48\) then \(y = 118x + 6\) → Incorrect (the slope should not be \(118\); this is a calculation error).
-
Bud's work:
- \(-8y = -11x - 48\); then \(y = -11x + 6\) → Incorrect (the slope should be positive, i.e., \(\frac{11}{8}x\) not \(-11x\)).
Conclusion:
All three individuals made mistakes in their calculations. The correct answer is:
None of them are correct.
1 answer