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=9x4 y = 9x - 4 . The slope-intercept form of a line is y=mx+b y = mx + b , where m m is the slope. Therefore, the slope of the given line is m=9 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 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 9 is 19 -\frac{1}{9} .

Final Answer

  • Slope of a parallel line: 9 \boxed{9}
  • Slope of a perpendicular line: 19 \boxed{-\frac{1}{9}}
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