Question

How do I write the equations of lines through the given point parallel to the given line and perpendicular to the given line?

Answer 1

First we find the slope of the original equation
4x - 2y = 3
-2y = -4x + 3
y = -4/-2x - 3/2
y = 2x - 3/2......slope here is 2

for a parallel line, we use the same slope
y = mx + b
slope(m) = 2
(2,1)...x = 2 and y = 1
now we sub and find b, the y int
1 = 2(2) + b
1 = 4 + b
1 - 4 = b
-3 = b
so ur parallel equation is : y = 2x - 3

for a perpendicular slope, we need the negative reciprocal. All that means is flip the slope and change the sign. So we have a slope of 2...the negative reciprocal we need is -1/2
y = mx + b
slope(m) = -1/2
(2,1)...x = 2 and y = 1
now we sub again
1 = -1/2(2) + b
1 = -1 + b
1 + 1 = b
2 = b
ur perpendicular line is : y = -1/2x + 2
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x + 4 = 0
x = -4....this is a vertical line with an undefined slope....sorry but I am not sure about this one