given the line L: 4x+2y=3 and the point P (2,-3), find an equation of a line through P that is: a) parallel to L b) perpendicular to Lplease help and explain each step thank you!!
The equation of the given line L is 4x + 2y = 3. Convert this into the slope-intercept form.
4x + 2y = 3
=> y = -(4/2)x + 3/2
The slope of the line is -2.
A line parallel to L will have the same slope as L. As it passes through the point (2, -3), we have [y - (-3)]/(x - 2) = -2
=> y + 3 = -2x + 4
=> 2x + y - 1 = 0
A line perpendicular to L has a slope m such that m*-2 = -1
=> m = 1/2
As this line passes through the point (2, -3), we have
(y + 3)/(x - 2) = 1/2
=> 2y + 6 = x - 2
=> x -2y - 8 = 0
The required equation of the parallel line is 2x + y - 1 = 0 and that of the perpendicular line is x - 2y - 8 = 0