Question

given the point 1 and 2 find the equation of a line on which it how many such equation are there

Answer 1

there can be infinite equations in a single line in graph paper.so the ans. of ur question. is simple that it will have infinite equations

Answer 2

Hola there,

Given two points P₁( x₁ , y₁ ) and P₂( x₂ , y₂ )

We know, equation of a line → ax + by + c = 0  ← ( i )

Put x = x₁ and y = y₁ to get :

→ ax₁ + by₁ + c = 0  ←  ( ii )

Again x = x₂ and y = y₂ gives :

→ ax₂ + by₂ + c = 0  ← ( iii )

Subtracting ( ii ) from ( iii ) →

a( x₂ - x₁ ) = b( y₂ - y₁ )

$=\ \textgreater \ \frac{x_2 - x_1}{y_2 - y_1} = \frac{b}{a}$

Again, repeat the same for ( i ) and ( ii ) to get :

$\frac{x-x_1}{y-y_1} = \frac{b}{a}$

Now, equating ( b / a ) from both eqn.s →

 $\frac{x-x_1}{y-y_1} = \frac{x_1 - x_2 }{y_1 - y_2 }$

From here, put the values of → [ x₁ , x₂ , y₁ , y₂ ] to get your equation

By the way, only one line passes straight through two defined points

Hope it helps ...:)