Question

the equation of line passing through (1 ,1) and (2,2) is​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Eqn\:of\:line=x-y=0}}}$

$\green{\tt{\therefore{Eqn\:of\:line=x+y-4=0}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies Points \: on \: line = (1,1) \: and \: (2,2) \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies Eqn \: of \: line = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies (y - y_{1}) = (\frac{ y_{2} - y_{1} }{x_{2} - x_{1}} )( x - x_{1}) \\ \\ \tt: \implies y - 1 = (\frac{2 - 1}{2 - 1} )( x - 1) \\ \\ \tt: \implies y - 1 = 1 \times (x - 1 ) \\ \\ \tt: \implies x - 1 + 1 - y = 0 \\ \\ \green{\tt: \implies x - y = 0} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies (y - y_{1}) = (\frac{ y_{2} - y_{1} }{x_{2} - x_{1}} )( x - x_{1}) \\ \\ \tt: \implies y -2 = (\frac{1 - 2}{ 1 - 2} )( x - 2) \\ \\ \tt: \implies y - 2 = - 1 \times (x - 2 ) \\ \\ \tt: \implies x - 2 - 2 + y = 0 \\ \\ \green{\tt: \implies x + y - 4= 0}$

Answer 2

$\tt {\huge {\pink{ Hello!!! }}}$

$\tt {\red { Given \: - }}$

The Line is passing through (1 ,1) and (2,2) .

Two Point Slope Equation :

$</p><p>\tt{\purple{\implies{y \: - \: y_{1} = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1} } \times x \: - \: x_{1} }}} ........(1)$

Here :

$</p><p>x_{1} = 1 \\ \\y_{1} = 1 \\ \\ x_{2} = 2 \\ \\ y_{2} = 2$

Placing the values in the above equation and solving we get the following lines :

$\tt {\orange{ \implies { x - y = 0 }}} .......(A_{1})$

$\tt {\orange{ \implies { x + y -4= 0 }}} .......(A_{2})$