Question

13.) Find the equation of a line through to
given pair of points (2,3) ad (-7,-1)​

Answer 1

Given :

Two points :- (2,3) ad (-7,-1)

To find :

equation of a line through to given pair of points (2,3) ad (-7,-1)

Formula used :

$\blue {\underline{\boxed{\bf \red { y - y _1 = (x - x _1)\bigg( \frac{y_2 - y _1}{x_2 - x _1} \bigg )}}}}$

Where :-

$\bigg( \bf\dfrac{y_2 - y _1}{x_2 - x _1} \bigg ) = slope \: of \: line$

Solution :

Two points are given as (2,3) ad (-7,-1).

$\sf \implies{ y - y _1 = (x - x _1)\bigg( \dfrac{y_2 - y _1}{x_2 - x _1} \bigg )}$

$\sf \implies{ y - 3= (x - 2)\bigg( \dfrac{- 1 - 3}{ - 7 - 2} \bigg )}$

$\sf \implies{ y - 3= (x - 2)\bigg( \dfrac{- 4}{ - 9} \bigg )}$

$\sf \implies{ y - 3= (x - 2)\bigg( \dfrac{ 4}{ 9} \bigg )}$

$\sf \implies9( y - 3)= (x - 2)4$

$\sf \implies9y - 27= 4x - 8$

$\sf \implies9y - 4x=27 - 8$

$\sf \implies9y - 4x=19$

Answer :

$\sf \implies9y - 4x - 19 = 0$

Answer 2

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HERE IS UR ANSWER

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Given :

Two points :- (2,3) ad (-7,-1)

To find :

equation of a line through to given pair of points (2,3) ad (-7,-1)

Formula used :

$\blue {\underline{\boxed{\bf \red { y - y _1 = (x - x _1)\bigg( \frac{y_2 - y _1}{x_2 - x _1} \bigg )}}}}\\y−y1=(x−x1)(x2−x1y2−y1)\\</p><p>Where :-\\</p><p>\bigg( \bf\dfrac{y_2 - y _1}{x_2 - x _1} \bigg ) = slope \: of \: line(x2−x1y2−y1)=slopeofline$

Solution :

Two points are given as (2,3) ad (-7,-1).

$\sf \implies{ y - y _1 = (x - x _1)\bigg( \dfrac{y_2 - y _1}{x_2 - x _1} \bigg )}⟹y−y1=(x−x1)(x2−x1y2−y1)\\</p><p>\sf \implies{ y - 3= (x - 2)\bigg( \dfrac{- 1 - 3}{ - 7 - 2} \bigg )}⟹y−3=(x−2)(−7−2−1−3)\\</p><p>\sf \implies{ y - 3= (x - 2)\bigg( \dfrac{- 4}{ - 9} \bigg )}⟹y−3=(x−2)(−9−4)\\</p><p>\sf \implies{ y - 3= (x - 2)\bigg( \dfrac{ 4}{ 9} \bigg )}⟹y−3=(x−2)(94)\\</p><p>\sf \implies9( y - 3)= (x - 2)4⟹9(y−3)=(x−2)4\\</p><p>\sf \implies9y - 27= 4x - 8⟹9y−27=4x−8\\</p><p>\sf \implies9y - 4x=27 - 8⟹9y−4x=27−8\\</p><p>\sf \implies9y - 4x=19⟹9y−4x=19$

Answer :

9y - 4x - 19 = 0⟹9y−4x−19=0