Answer :
To determine the slope of a line that is perpendicular to a given line, we need to understand that perpendicular lines have slopes that are negative reciprocals of each other.
Given the equation of the line:
[tex]\[ y = 2x - 6 \][/tex]
From this equation, we can clearly see that the slope (m) of this line is 2.
Now, to find the slope of a line that is perpendicular to this one, we need to find the negative reciprocal of the slope 2.
The reciprocal of 2 is [tex]\( \frac{1}{2} \)[/tex], and taking the negative of this gives us:
[tex]\[ -\frac{1}{2} \][/tex]
So, the slope of the line that is perpendicular to the line [tex]\( y = 2x - 6 \)[/tex] is:
[tex]\[ -\frac{1}{2} \][/tex]
Therefore, the correct answer is:
D. [tex]\( -\frac{1}{2} \)[/tex]
Given the equation of the line:
[tex]\[ y = 2x - 6 \][/tex]
From this equation, we can clearly see that the slope (m) of this line is 2.
Now, to find the slope of a line that is perpendicular to this one, we need to find the negative reciprocal of the slope 2.
The reciprocal of 2 is [tex]\( \frac{1}{2} \)[/tex], and taking the negative of this gives us:
[tex]\[ -\frac{1}{2} \][/tex]
So, the slope of the line that is perpendicular to the line [tex]\( y = 2x - 6 \)[/tex] is:
[tex]\[ -\frac{1}{2} \][/tex]
Therefore, the correct answer is:
D. [tex]\( -\frac{1}{2} \)[/tex]
