Question

Give the equation of two lines passing through $(2,10)$.

Answer 1

We have to form equation of two lines passing through $(2,10)$.

i.e., the point $(2,10)$ should satisfies the required equations.

lets observe the sum of the coordinates of the points,

$2+10=12$

$\Rightarrow$ One of the equation of line is

$x+y=12$ ---(1)

$2-10=-8$

$\Rightarrow$ one more equation of the line is

$x-y=-8$ or $y-x=8$----(2)

Since, there exist infinite number of lines passing through a point.

we can create the infinite number of equation of lines.

ex:

Point is $(2,10)$

$5\left(2\right)-3\left(10\right)=10-30=-20$

i.e., $5x-3y=-20$ is also passing through the point $(2,10)$.