The equation of the perpendicular line is y = (1/8)x + 15/4.
We are given the equation of a straight line. The equation is y = -8x - 3. The slope of the given line is -8. We need to find the equation of the straight line that is perpendicular to the given line and passes through the coordinates (2, 4).
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line. Let the slope of the perpendicular line be represented by the variable "m".
m = -1/(-8) = 1/8
The equation of the perpendicular line using the slope-point form can be written as given below.
y = mx + c
y = (1/8)x + c
The line passes through the point (2, 4).
4 = (1/8)2 + c
4 = (1/4) + c
c = 4 - (1/4)
c = 15/4
Hence, the equation of the perpendicular line is y = (1/8)x + 15/4.
The complete question is given below.
Write an equation of the line that passes through point p and is perpendicular to the line with the given equation.
P (2, 4)
y = -8x - 3
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