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:
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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 \( -\frac{1}{m} \).
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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!