Question
Coordinate Proofs Quick Check 3 of 53 of 5 Items Question Use the image to answer the question. Calculate the equation of a line that is perpendicular to the line shown on the graph and that also shares the same y-intercept. (1 point) Responses y=−2x+4 y equals negative 2 x plus 4 y=12x−8 y equals Start Fraction 1 over 2 End Fraction x minus 8 y=−12x+4 y equals negative Start Fraction 1 over 2 End Fraction x plus 4 y=2x−8 y equals 2 x minus 8 Skip to navigation page 18 of 18 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
Answers
GPT-4o mini
To find the equation of the line that is perpendicular to the line shown on the graph and shares the same y-intercept, we need to follow these steps:
1. **Identify the slope of the given line**: If the slope of the given line is \( m \), the slope of the line that is perpendicular to it will be \( -\frac{1}{m} \).
2. **Find the y-intercept**: The y-intercept is the value of y when x = 0.
Assuming we don’t have the graph to analyze, let’s consider a sample scenario:
- If the equation of the original line is \( y = mx + b \), then:
- The slope \( m \) and the y-intercept \( b \) would determine the perpendicular line.
- The perpendicular line would have the slope \( -\frac{1}{m} \) and the same y-intercept \( b \).
### Example:
If the original line's equation is \( y = 2x + 4 \):
- Slope \( m = 2 \).
- The perpendicular slope would be \( -\frac{1}{2} \).
- Y-intercept \( b = 4 \).
- The equation of the perpendicular line would be \( y = -\frac{1}{2}x + 4 \).
If you could provide the slope of the original line from the image or any values that are visible (like coordinates of points), I could help calculate the exact equation for you. Without this information, I can guide you through how to derive it!
1. **Identify the slope of the given line**: If the slope of the given line is \( m \), the slope of the line that is perpendicular to it will be \( -\frac{1}{m} \).
2. **Find the y-intercept**: The y-intercept is the value of y when x = 0.
Assuming we don’t have the graph to analyze, let’s consider a sample scenario:
- If the equation of the original line is \( y = mx + b \), then:
- The slope \( m \) and the y-intercept \( b \) would determine the perpendicular line.
- The perpendicular line would have the slope \( -\frac{1}{m} \) and the same y-intercept \( b \).
### Example:
If the original line's equation is \( y = 2x + 4 \):
- Slope \( m = 2 \).
- The perpendicular slope would be \( -\frac{1}{2} \).
- Y-intercept \( b = 4 \).
- The equation of the perpendicular line would be \( y = -\frac{1}{2}x + 4 \).
If you could provide the slope of the original line from the image or any values that are visible (like coordinates of points), I could help calculate the exact equation for you. Without this information, I can guide you through how to derive it!