Questions: A line is perpendicular to (y=2 x-7) What is the slope of the perpendicular line? (-1 / 2)

A line is perpendicular to (y=2 x-7) What is the slope of the perpendicular line? (-1 / 2)
Transcript text: A line is perpendicular to $y=2 x-7$ What is the slope of the perpendicular line? $-1 / 2$
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Solution

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Solution Steps

To find the slope of a line that is perpendicular to another line, we need to use the concept of negative reciprocals. The slope of the given line is 2. The slope of the perpendicular line will be the negative reciprocal of 2.

Step 1: Identify the Slope of the Given Line

The equation of the given line is \( y = 2x - 7 \). The slope of this line is the coefficient of \( x \), which is \( 2 \).

Step 2: Calculate the Slope of the Perpendicular Line

To find the slope of a line that is perpendicular to another line, we take the negative reciprocal of the given slope. The negative reciprocal of \( 2 \) is \( -\frac{1}{2} \).

Final Answer

The slope of the perpendicular line is \( \boxed{-\frac{1}{2}} \).

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