Question

Give equation of two lines passing through $\left(2,14\right)$. How many more such lines are there$?$ and why$?$

Answer 1

Step1- Finding equation of two lines through point $\left(2,14\right)$:

The linear equation in two variables is given in form of $ax+by+c=0$

The given point is $\left(2,14\right)$ where $x=2$ and $y=14$

The first equation can be ,

$\Rightarrow x+y=2+14$

$\Rightarrow x+y=16$

The second equation can be

;$\Rightarrow x-y=2-14$

$\Rightarrow x-y=-12$

Therefore , two equation of lines passing through point $\left(2,14\right)$ is $x+y=16$ and $x-y=-12$.

Step2- Finding the number of lines to be passed through point $\left(2,14\right)$.

A linear equation in two variable can have infinite solutions.

similarly for the solution $\left(2,14\right)$ we can find infinite equations

Therefore infinite lines can pass through the point $\left(2,14\right)$.