Questions: What is the slope of a line perpendicular to the line y=12/5 x+4 ? a.) -12/5 b.) -5/12 c.) -4 d.) -1/4

What is the slope of a line perpendicular to the line y=12/5 x+4 ? a.) -12/5 b.) -5/12 c.) -4 d.) -1/4
Transcript text: What is the slope of a line perpendicular to the line $y=\frac{12}{5} x+4$ ? a.) $-\frac{12}{5}$ b.) $-\frac{5}{12}$ c.) -4 d.) $-\frac{1}{4}$
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Solution

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Solution Steps

To find the slope of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line. The given line is in the form \( y = mx + b \), where \( m \) is the slope. For the line \( y = \frac{12}{5}x + 4 \), the slope \( m \) is \( \frac{12}{5} \). The negative reciprocal of \( \frac{12}{5} \) is \( -\frac{5}{12} \).

Step 1: Identify the Slope of the Given Line

The equation of the given line is \( y = \frac{12}{5}x + 4 \). From this equation, we can identify the slope \( m \) of the line as \( \frac{12}{5} \).

Step 2: Calculate the Slope of the Perpendicular Line

To find the slope of a line that is perpendicular to the given line, we take the negative reciprocal of the slope \( m \). Thus, the slope of the perpendicular line is calculated as follows: \[ m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{\frac{12}{5}} = -\frac{5}{12} \]

Final Answer

The slope of the line perpendicular to the given line is \\(\boxed{-\frac{5}{12}}\\).

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