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Question

Find the equation of the line joining the point (3, 5) to the point of intersection of the lines 4 x+y1=0 and 7 x3 y35=0.

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Solution

The point of intersection of the lines

4x+y1=0 and 7x3y35=0 is

y=14x

7x3(14x)35=0

7x3+12x35=0

19x38

x=2

y=14x=18=7

Let P(2, 7) and Q(3, 5)

The equation of line PQ is

yy1=m(xx1)

yy1=y2y1x2x1(xx1)

y(7)=5(7)32(x2)

y+7=12(x2)

y=12x=31

12xy31=0


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