To find the equation of a line that is perpendicular to a given line and shares the same y-intercept, you first need to find the slope of the given line.
Steps:
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Identify the slope of the given line. If the equation of the line is in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, the slope is straightforward.
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Calculate the perpendicular slope. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. If the slope of the given line is \(m\), the slope of the line that is perpendicular would be \(-\frac{1}{m}\).
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Write the new line's equation. Since we want this new line to have the same y-intercept \(b\), we can use the point-slope form of a line or the slope-intercept form \(y = mx + b\).
Example Calculation:
Let's assume the original line has the equation \(y = 2x + 4\) (just as an example since the original line isn't provided in your question).
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Find the slope of the original line:
- From \(y = 2x + 4\), the slope \(m = 2\).
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Calculate the perpendicular slope:
- The negative reciprocal of \(2\) is \(-\frac{1}{2}\).
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Write the new line's equation with the same y-intercept \(4\):
- The equation becomes: \[ y = -\frac{1}{2}x + 4 \]
Conclusion:
If the original line's equation is \(y = mx + 4\) where \(m\) can be substituted based on your original equation, the resulting equation of the line that is perpendicular and shares the same y-intercept is \(y = -\frac{1}{m}x + 4\).
If you provide the original line's equation, I can give you the specific solution for that case.
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