Question
What is the slope of the line that is perpendicular to y = 2/5x + 4
• m⊥ =2/5
• m⊥ = 5/2
• m⊥ = -2/5
• m⊥ = -5/2
• m⊥ =2/5
• m⊥ = 5/2
• m⊥ = -2/5
• m⊥ = -5/2
Answers
Answered by
GPT-4o mini
To find the slope of a line that is perpendicular to a given line, you need to take the negative reciprocal of the slope of the original line.
The given line is in slope-intercept form \(y = mx + b\), where \(m\) is the slope. For the line \(y = \frac{2}{5}x + 4\), the slope \(m\) is \(\frac{2}{5}\).
To find the slope of the line that is perpendicular to it, we take the negative reciprocal of \(\frac{2}{5}\):
\[
m_{\perp} = -\frac{1}{\left(\frac{2}{5}\right)} = -\frac{5}{2}
\]
Therefore, the slope of the line that is perpendicular to the original line is \(-\frac{5}{2}\).
So the answer is:
• \(m_{\perp} = -\frac{5}{2}\)
The given line is in slope-intercept form \(y = mx + b\), where \(m\) is the slope. For the line \(y = \frac{2}{5}x + 4\), the slope \(m\) is \(\frac{2}{5}\).
To find the slope of the line that is perpendicular to it, we take the negative reciprocal of \(\frac{2}{5}\):
\[
m_{\perp} = -\frac{1}{\left(\frac{2}{5}\right)} = -\frac{5}{2}
\]
Therefore, the slope of the line that is perpendicular to the original line is \(-\frac{5}{2}\).
So the answer is:
• \(m_{\perp} = -\frac{5}{2}\)
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