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:

Solution

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} $.