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 - incorrect
y=−14x−8
y is equal to negative 1 fourth x minus 8 - no response given
y=14x−5
y is equal to 1 fourth x minus 5 - no response given
y=−5
(1 point)
Responses
y=14x−8
y is equal to 1 fourth x minus 8 - incorrect
y=−14x−8
y is equal to negative 1 fourth x minus 8 - no response given
y=14x−5
y is equal to 1 fourth x minus 5 - no response given
y=−5
Answers
Answered by
GPT-4o mini
To shift a graph down by a certain number of units, you subtract that number from the entire equation.
If we take the equation \( y = f(x) \) and shift it down by 8 units, the new equation becomes:
\[ y = f(x) - 8 \]
Now, to determine which of the responses given reflects a downward shift of 8 units, we need to examine the format of each option.
1. **y = 14x - 8**: This does not show a downward shift because the -8 is not subtracted from \( y \).
2. **y = (1/4)x - 8**: This indicates a downward shift of 8 units from the original equation \( y = (1/4)x \).
3. **y = -14x - 8**: Similarly, the -8 at the end does not indicate a downward shift from an original equation.
4. **y = (1/4)x - 5**: This does not reflect a downward shift of 8 units as it is only shifted down 5 units.
5. **y = -5**: This is a constant line at y = -5 and doesn't indicate a shift of the formula at all.
Based on this reasoning, the correct answer is:
**y = (1/4)x - 8**.
This option shows a graph that has been shifted down by 8 units from its original position.
If we take the equation \( y = f(x) \) and shift it down by 8 units, the new equation becomes:
\[ y = f(x) - 8 \]
Now, to determine which of the responses given reflects a downward shift of 8 units, we need to examine the format of each option.
1. **y = 14x - 8**: This does not show a downward shift because the -8 is not subtracted from \( y \).
2. **y = (1/4)x - 8**: This indicates a downward shift of 8 units from the original equation \( y = (1/4)x \).
3. **y = -14x - 8**: Similarly, the -8 at the end does not indicate a downward shift from an original equation.
4. **y = (1/4)x - 5**: This does not reflect a downward shift of 8 units as it is only shifted down 5 units.
5. **y = -5**: This is a constant line at y = -5 and doesn't indicate a shift of the formula at all.
Based on this reasoning, the correct answer is:
**y = (1/4)x - 8**.
This option shows a graph that has been shifted down by 8 units from its original position.