To find the slope of a line that is perpendicular to the given line [tex]\( y = \frac{3}{4}x - 6 \)[/tex], we need to perform a few steps.
1. Identify the slope of the given line:
The equation of the line is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope of the line. Here, the slope [tex]\( m \)[/tex] of the given line is [tex]\( \frac{3}{4} \)[/tex].
2. Determine the slope of the perpendicular line:
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. The negative reciprocal is found by taking the opposite sign and flipping the fraction.
For the slope [tex]\( \frac{3}{4} \)[/tex], the negative reciprocal is:
[tex]\[
-\frac{1}{\frac{3}{4}} = -\frac{4}{3}
\][/tex]
3. Identify the correct answer:
From the given options:
A. [tex]\( -\frac{4}{3} \)[/tex]
B. [tex]\( \frac{1}{6} \)[/tex]
C. [tex]\( \frac{3}{4} \)[/tex]
D. [tex]\( -\frac{3}{4} \)[/tex]
The slope of the line that is perpendicular to the given line [tex]\( y = \frac{3}{4} x - 6 \)[/tex] is [tex]\( -\frac{4}{3} \)[/tex].
Thus, the correct answer is:
A. [tex]\( -\frac{4}{3} \)[/tex]
