Question

Find the equation of the line passing through the intersection of 3x-2y=6 with the x-axis and parallel to the line 2x-y-1=0

Answer 1

As 3x-2y-6=0 and 2x-y-1=0 are parallel then
3x-2y-6=2x-y-1
or 3x-2x-2y+y=-1+6
or x-y=5 [ since line passes through the x-axis then the coordinates of the point is (x, 0) i. e., y=0]
or x-0=5
or x=5
Therefore, slope of 3 x-2y- 6 =slope of 2 x- y-1
the slope is 3/2
We know that, y-y1 = m(x-x1)
Therefore, y-0= 3/2(x-5)
or 2y= (3x-15)
the equation of a line is
3x-2y-15=0
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