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Question

Find the equation of a line which is parallel to the line 2x+3y−6=0 and the sum of the intercepts on the axes is 10.

A
2x+3y=12
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B
x+3y=9
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C
3x+2y=8
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D
2x+3y=8
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Solution

The correct option is A 2x+3y=12
The equation of a line in form of intercepts on coordinate axes is given by, xa+yb=1

Slope of the line written above is m=ba

If according to given conditions the line is parallel to line 2x+3y6=0, then their slopes must me equal.

Hence m=ba=23

2a=3b

The sum of the intercepts on axes .i.e. a+b=10 (Given)

using above two results we can write a+23a=10

a=6

b=4

Then the equatiuon of line will be x6+y4=1

2x+3y=12

Correct answer is A

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