Question

Given the linear equation $2x+3y-8=0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines.

Answer 1

Given line is $2x+3y-8=0$

(a)example of intersecting line ;

$x+y-5=0$ forms a intersecting line

(b) example for parallel line

Parallel line $\Rightarrow$slopes must be equal

$\Rightarrow 6x+9y+10=0$ is parallel to the given line

(c) example of coincident lines

Coincident $\Rightarrow$ratio of coefficient must be equal

$\Rightarrow 4x+6y-16=0$ coincides with the given line