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!!

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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