A line contains the points (−4, −13) and (−2, 3). What is the slope of a line that is perpendicular to this line?
−1/8
1/8
−8
I do not know the answer yet.
8
A line contains the points (−4, −13) and (−2, 3). What is the slope of a line that is perpendicular to this line?
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To find the slope of a line that is perpendicular to the given line, we first need to determine the slope of the line that passes through the points (−4, −13) and (−2, 3).
The formula for the slope (m) between two points ((x_1, y_1)) and ((x_2, y_2)) is:
[
m = frac{y_2 – y_1}{x_2 – x_1}
]
Plugging in our points:
[
m = frac{3 – (-13)}{-2 – (-4)} = frac{3 + 13}{-2 + 4} = frac{16}{2} = 8
]
The slope of the original line is 8.
Lines that are perpendicular have slopes that are negative reciprocals of each other. Therefore, to find the slope of the perpendicular line, we take the negative reciprocal of 8:
[
text{slope of perpendicular line} = -frac{1}{8}
]
Thus, the answer is (-frac{1}{8}).