**Student:** Vaishnavi Gupta

**Q. Give the equations of two lines passing through (2, 14). Calculate how many more such lines are there also give reason?**

**Answer : **

Hi Vaishnavi, Thanks for your query.

**Topic: Geometry, Equation of line**

**Core Concept:**

*The Greek Mathematician of Euclid`s time derived the notion of point, line, plane etc. from what they have seen around them. They thought of Geometry as an abstract model of world they lived in. *

*From studies of the space and solids in the space around them, an abstract geometrical notion of a solid object was developed.*

*Consider the three steps from solids to points (solids-surfaces-lines-points). In each step we lose one extension, also called a dimension. So, a solid has three dimensions, a surface has two, a line has one and a point has none.*

Euclid summarized these statements as definitions.

- A point is that which has no part.
- A line is breadthless length.

As per Euclid`s Axioms : *Point is that which has no part.*

So there can be infinite number of lines passing through a given point as you can visibly see also.

**Method and Solution :**

Given the point (2,14), there can be infinite lines passing through it. Here are two examples of equation of lines as you have asked:

* y-x=12
x+y = 16*

**More Examples : **

*2x+y= 18*

*9x-y=4*

*7x-y=0*

Idea is that the given point shall satisfy the equation.