Questions: Consider the line (y=9 x-4) What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: Slope of a perpendicular line:

Consider the line (y=9 x-4) What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: Slope of a perpendicular line:
Transcript text: Consider the line $y=9 x-4$ What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: Slope of a perpendicular line:
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Solution

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Solution Steps

Step 1: Identify the Slope of the Given Line

The given line equation is \( y = 9x - 4 \). The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. Therefore, the slope of the given line is \( m = 9 \).

Step 2: Determine the Slope of a Parallel Line

Lines that are parallel have the same slope. Thus, the slope of a line parallel to the given line is also \( 9 \).

Step 3: Determine the Slope of a Perpendicular Line

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The negative reciprocal of \( 9 \) is \( -\frac{1}{9} \).

Final Answer

  • Slope of a parallel line: \( \boxed{9} \)
  • Slope of a perpendicular line: \( \boxed{-\frac{1}{9}} \)
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