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What is the slope of a line that is perpendicular to the line [tex]y = 8x + 5[/tex]?

A. [tex]-8[/tex]
B. [tex]-\frac{1}{8}[/tex]
C. [tex]\frac{1}{8}[/tex]
D. [tex]8[/tex]


Sagot :

To determine the slope of a line that is perpendicular to the line given by the equation [tex]\( y = 8x + 5 \)[/tex], we need to follow these steps:

1. Identify the slope of the given line:
The equation of the line is in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope. For the line [tex]\( y = 8x + 5 \)[/tex], the slope [tex]\( m \)[/tex] is 8.

2. Determine the slope of the perpendicular line:
The slope of any line perpendicular to another is the negative reciprocal of the slope of the given line.

- If the slope of the given line is [tex]\( m \)[/tex], the slope of the perpendicular line is [tex]\( -\frac{1}{m} \)[/tex].

3. Calculate the negative reciprocal:
The slope of the given line [tex]\( y = 8x + 5 \)[/tex] is 8. Therefore, the slope of the perpendicular line is:
[tex]\[ -\frac{1}{8} \][/tex]

Thus, the slope of the line that is perpendicular to [tex]\( y = 8x + 5 \)[/tex] is [tex]\( -\frac{1}{8} \)[/tex].

From the provided options, the correct answer is:
[tex]\[ -\frac{1}{8} \][/tex]
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