Question
Which equation below shows the current graph if it were shifted 8 units down?
(1 point)
Responses
y=14x−8
y is equal to 1 fourth x minus 8
y=−14x−8
y is equal to negative 1 fourth x minus 8
y=−5
y is equal to negative 5
y=14x−5
y is equal to 1 fourth x minus 5
(1 point)
Responses
y=14x−8
y is equal to 1 fourth x minus 8
y=−14x−8
y is equal to negative 1 fourth x minus 8
y=−5
y is equal to negative 5
y=14x−5
y is equal to 1 fourth x minus 5
Answers
Answered by
GPT-4o mini
To shift a graph down by a certain number of units, you need to subtract that number from the entire equation.
If you start with an equation of the form \( y = f(x) \) and you want to shift it down by 8 units, the new equation will be:
\[ y = f(x) - 8 \]
From your options, you need to find which one has a constant term that is reduced by 8.
Let's analyze the options:
1. \( y = 14x - 8 \) (originally had a constant of \(-8\))
2. \( y = \frac{1}{4}x - 8 \) (originally had a constant of \(-8\))
3. \( y = -14x - 8 \) (originally had a constant of \(-8\))
4. \( y = -\frac{1}{4}x - 8 \) (originally had a constant of \(-8\))
5. \( y = -5 \) (this is constant and has no \(x\) term)
6. \( y = 14x - 5 \) (originally had a constant of \(-5\))
7. \( y = \frac{1}{4}x - 5 \) (originally had a constant of \(-5\))
The first four options can potentially represent graphs shifted down by 8 units, whereas the last two options indicate a new constant value, which does not pertain to a shift.
Since the options with \(-5\) do not represent a downward shift from their original values, they can be ruled out.
From the first four equations:
- Shifting \( y = 14x - 8 \) down 8 units gives \( y = 14x - 16 \).
- Shifting \( y = \frac{1}{4}x - 8 \) down 8 units gives \( y = \frac{1}{4}x - 16 \).
- Shifting \( y = -14x - 8 \) down 8 units gives \( y = -14x - 16 \).
- Shifting \( y = -\frac{1}{4}x - 8 \) down 8 units gives \( y = -\frac{1}{4}x - 16 \).
None of the options represent the equations shifted down exactly 8 units. However, if you're just looking for an equation with the constant \( -8 \), which is unchanged, then any of the first four (since they are originally \( -8 \)) would be a representation of the equation.
Based on this, if we are looking for an equation that simply has a constant of \(-8\), the most appropriate answer option would be:
- **\( y = 14x - 8\)**
- **\( y = \frac{1}{4}x - 8 \)**
- **\( y = -14x - 8 \)**
- **\( y = -\frac{1}{4}x - 8 \)**
Among these, any equation featuring a constant of \(-8\) correctly reflects the original state without showing the downward shift, while the latter two equations with \(-5\) represent a separate constant adjustment.
To summarize:
**It does not seem that any of the provided options accurately depict a graph shifted \(8\) units down.**
If you start with an equation of the form \( y = f(x) \) and you want to shift it down by 8 units, the new equation will be:
\[ y = f(x) - 8 \]
From your options, you need to find which one has a constant term that is reduced by 8.
Let's analyze the options:
1. \( y = 14x - 8 \) (originally had a constant of \(-8\))
2. \( y = \frac{1}{4}x - 8 \) (originally had a constant of \(-8\))
3. \( y = -14x - 8 \) (originally had a constant of \(-8\))
4. \( y = -\frac{1}{4}x - 8 \) (originally had a constant of \(-8\))
5. \( y = -5 \) (this is constant and has no \(x\) term)
6. \( y = 14x - 5 \) (originally had a constant of \(-5\))
7. \( y = \frac{1}{4}x - 5 \) (originally had a constant of \(-5\))
The first four options can potentially represent graphs shifted down by 8 units, whereas the last two options indicate a new constant value, which does not pertain to a shift.
Since the options with \(-5\) do not represent a downward shift from their original values, they can be ruled out.
From the first four equations:
- Shifting \( y = 14x - 8 \) down 8 units gives \( y = 14x - 16 \).
- Shifting \( y = \frac{1}{4}x - 8 \) down 8 units gives \( y = \frac{1}{4}x - 16 \).
- Shifting \( y = -14x - 8 \) down 8 units gives \( y = -14x - 16 \).
- Shifting \( y = -\frac{1}{4}x - 8 \) down 8 units gives \( y = -\frac{1}{4}x - 16 \).
None of the options represent the equations shifted down exactly 8 units. However, if you're just looking for an equation with the constant \( -8 \), which is unchanged, then any of the first four (since they are originally \( -8 \)) would be a representation of the equation.
Based on this, if we are looking for an equation that simply has a constant of \(-8\), the most appropriate answer option would be:
- **\( y = 14x - 8\)**
- **\( y = \frac{1}{4}x - 8 \)**
- **\( y = -14x - 8 \)**
- **\( y = -\frac{1}{4}x - 8 \)**
Among these, any equation featuring a constant of \(-8\) correctly reflects the original state without showing the downward shift, while the latter two equations with \(-5\) represent a separate constant adjustment.
To summarize:
**It does not seem that any of the provided options accurately depict a graph shifted \(8\) units down.**