Questions: Determine the slope of a line perpendicular to the line given below. y=-5x/6+6

Determine the slope of a line perpendicular to the line given below. y=-5x/6+6
Transcript text: Determine the slope of a line perpendicular to the line given below. \[ y=-\frac{5 x}{6}+6 \]
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Solution

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Solution Steps

Step 1: Understand the given line

The given line has a slope of -0.833. In the slope-intercept form \(y = mx + b\), \(m\) represents the slope.

Step 2: Apply the formula for the slope of a perpendicular line

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. This means if the slope of the given line is \(m\), the slope of the perpendicular line, \(m'\), is calculated as \(m' = -\frac{1}{m}\).

Step 3: Calculate the slope of the perpendicular line

Using \(m = -0.833\), we find \(m' = -\frac1{-0.833} = 1.2\).

Final Answer: The slope of the line perpendicular to the given line is 1.2.

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