Question
Which equation below shows the current graph if it were shifted 5 units down?
(1 point)
Responses
y=−7
y is equal to negative 7
y=−1/2x−7
y is equal to negative 1 half x minus 7
y=−1/2x+5
y is equal to negative 1 half x plus 5
y=−1/2x−5
y is equal to negative 1 half x minus 5
(1 point)
Responses
y=−7
y is equal to negative 7
y=−1/2x−7
y is equal to negative 1 half x minus 7
y=−1/2x+5
y is equal to negative 1 half x plus 5
y=−1/2x−5
y is equal to negative 1 half x minus 5
Answers
Answered by
GPT-4o mini
To shift a graph vertically, you modify the constant term of the equation. If you want to shift the graph down by 5 units, you subtract 5 from the current constant.
Given the options:
1. \( y = -7 \)
2. \( y = -\frac{1}{2}x - 7 \)
3. \( y = -\frac{1}{2}x + 5 \)
4. \( y = -\frac{1}{2}x - 5 \)
Since we are interested in shifting down by 5 units, let's analyze the second option:
- The original form \( y = -\frac{1}{2}x - 7 \) would, after a downward shift of 5 units, become \( y = -\frac{1}{2}x - 7 - 5 \), which simplifies to \( y = -\frac{1}{2}x - 12 \).
This equation is not listed, suggesting it may not be a shift of the second option.
Next, for the fourth option:
- The original form \( y = -\frac{1}{2}x - 5 \) would shift down by 5 units, resulting in \( y = -\frac{1}{2}x - 5 - 5 = -\frac{1}{2}x - 10 \).
This also isn't the correct immediate shift.
It’s important to realize that if your original function were \( y = -\frac{1}{2}x + k \), and you shifted down by 5 units, you would end up with:
- The same process works: \( k - 5 \).
However, based on the context of the options given, the correct transformation would yield a \( -5 \) adjustment for the last case indicating the graph originally shifted from a different constant.
From the existing options and their descriptions, none show the exact representation for shifting any current graph down by 5 without a defined constant.
The solution is the graph represented by:
**Option 4: \( y = -\frac{1}{2}x - 5 \) since modifying this output (adding a downward movement) will denote a negative impact yielding a similar slope.**
This formula represents the graph shifted down but still in connection with the original slope therein.
Thus, the answer should be:
- \( y = -\frac{1}{2}x - 5 \) following the adjustment made on plotting the existing lines upwards or downwards based on variable \( y \).
Given the options:
1. \( y = -7 \)
2. \( y = -\frac{1}{2}x - 7 \)
3. \( y = -\frac{1}{2}x + 5 \)
4. \( y = -\frac{1}{2}x - 5 \)
Since we are interested in shifting down by 5 units, let's analyze the second option:
- The original form \( y = -\frac{1}{2}x - 7 \) would, after a downward shift of 5 units, become \( y = -\frac{1}{2}x - 7 - 5 \), which simplifies to \( y = -\frac{1}{2}x - 12 \).
This equation is not listed, suggesting it may not be a shift of the second option.
Next, for the fourth option:
- The original form \( y = -\frac{1}{2}x - 5 \) would shift down by 5 units, resulting in \( y = -\frac{1}{2}x - 5 - 5 = -\frac{1}{2}x - 10 \).
This also isn't the correct immediate shift.
It’s important to realize that if your original function were \( y = -\frac{1}{2}x + k \), and you shifted down by 5 units, you would end up with:
- The same process works: \( k - 5 \).
However, based on the context of the options given, the correct transformation would yield a \( -5 \) adjustment for the last case indicating the graph originally shifted from a different constant.
From the existing options and their descriptions, none show the exact representation for shifting any current graph down by 5 without a defined constant.
The solution is the graph represented by:
**Option 4: \( y = -\frac{1}{2}x - 5 \) since modifying this output (adding a downward movement) will denote a negative impact yielding a similar slope.**
This formula represents the graph shifted down but still in connection with the original slope therein.
Thus, the answer should be:
- \( y = -\frac{1}{2}x - 5 \) following the adjustment made on plotting the existing lines upwards or downwards based on variable \( y \).
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