Question

Give the equations of two lines passing through $(2,14)$. How many more such lines are there, and why?

Answer 1

Step 1: Evaluate the first equation

Given points is $(2,14)$.

Therefore,

$x=2$ and $y=14$

Then the first equation will be

$x+y$

$\Rightarrow 2+14=16$

$\therefore x+y=16$

Step 2: Evaluate the second equation

The second equation will be

$x-y$

$\Rightarrow 2-14=-12$

$\therefore x-y=-12$

Step 3: Evaluate the number of lines

We know that infinite lines can pass through one point.

Therefore, infinite more lines can pass through the point $(2,14)$.

Hence, the equations of two lines passing through $(2,14)$ are $x+y=16$ and $x-y=-12$ and there can be an infinite number of lines.