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the no. of lines that are parallel to 2x+6y-7=0 and have an intercept 10 between the coordinate axes is

The given equation of line is as,2x+6y-7=0          ....1⇒6y=-2x+7⇒y=-13x+76⇒The slope of the equation m=-13Thus, equation of line which is parallel to equation 1,y=-13x+c          ....2⇒x3c+yc=1x-intercept=3c,0y-intercept=0,cSince distance between co-ordinate axes=10Therefore,3c-02+0-c2=10⇒3c-02+0-c2=100⇒10c2=100⇒c=±10Substitute value of x in equation 2, we have,y=-13x±10Hence, there are two number of lines that are parallel to 2x+6y-7=0.

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