Question

Write the equation of three lines passing through$(2,–3)$.

Answer 1

Finding the required equation:

As we know, from any point infinite numbers of lines can pass.

For finding the equation, putting $x=2$ and $y=-3$in any equation and get RHS accordingly.

Hence the required equations are

$\left(i\right)$ $x+y-4=-5$

$\Rightarrow x+y=-5+4$

$\Rightarrow x+y=-1$

$\left(ii\right)$ $x-y-10=-5$

$\Rightarrow x-y=-5+10$

$\Rightarrow x-y=5$

$\left(iii\right)$$2x+y+7=8$

$\Rightarrow 2x+y=8-7$

$\Rightarrow 2x+y=1$

Similarly, we can find many more.

Hence, $x+y=-1$, $x-y=5$$\&2x+y=1$are the equations of three lines passing through$(2,–3)$.