In the equation of the line parallel to the line 2x - 3y=1 And passing through the middle point of the line segment joining the Points (1,3) and (1,-7) is

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Solution

Equation of the given line is
2x-3y=1
2x-1=3y
y=(2/3)x-(1/3)
comparing with the equation
y=mx +c
m=2/3
hence slope of the parallel line also =2/3
midpoint of the line
M=(x1+x2)/2,(y1+y2)/2
Using this equation
=(1+1)/2,(3-7)/2
=(1,-2)
Then we have to find c in the equation
y=mx+c
-2=(2/3)×1+c
c=-2-(2/3)
c=-(8/3)
Here we get
m=2/3
c=-(8/3)
put in the equation
y=mx+c
y=(2/3)x-(8/3)
multiplying with 3
3y=2x-8
Rearranging
2x-3y=8
equation of the required line is
2x-3y=8

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