Respuesta :
The line that is perpendicular to the line passing through the points (-4, 2) and (4, -1) is y = (8/3)x + 1/2
Equation of a line
From the question, we are to determine the equation of the line that is perpendicular to the line passing through the given points
First, we will determine the equation of the line passing through the given points
The given points are (-4, 2) and (4, -1)
Using the formula,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
x₁ = -4
y₁ = 2
x₂ = 4
y₂ = -1
Thus,
(y - 2)/(x - -4) = (-1 - 2)/(4 - -4)
(y - 2)/(x + 4) = (-3)/(4 + 4)
(y - 2)/(x + 4) = (-3)/(8)
8(y -2) = -3(x + 4)
8y - 16 = -3x -12
8y = -3x -12 + 16
8y = -3x + 4
y = -(3/8)x + 1/2
Now,
NOTE: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line
In the above equation,
The slope of the line is -3/8
∴ The slope of the line that is perpendicular to the line will be 8/3
Thus,
The equation of the line will be y = (8/3)x + 1/2
Hence, the line that is perpendicular to the line passing through the points (-4, 2) and (4, -1) is y = (8/3)x + 1/2
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