Question

What is the equation of the line that passes through the points (4,-1 ) and (-7,4 )?

Answer 1

`\large{ \tt{❃ \: STEP- BY - STEP \: EXPLANATION}} :`

• Let the equation of line passes through the points A ( 4 , - 1 ) and B ( - 7 , 4 ) . Let A ( 4 , -1 ) be ( x₁ , y₁ ) & B ( - 7 , 4 ) be ( x₂ , y₂ )

`\large{ \tt{❁ \: LET'S \: START}} :`

• Using two - point form of the equation of straight line , we have :

`\boxed{ \large{ \bf{❀ \: y -y _(1) = (y_(2) - y_(1) )/(x_(2) - x_(1)) (x - x_(1))}}}`

- Plug the values :

`\large{ \bf{⇢ \: y - ( - 1) = (4 - ( - 1))/( - 7 - 4)(x - 4) }}`

`\large{ \bf{⇢y + 1 = (4 + 1)/( - 11) (x - 4)}}`

`\large{ \bf{⇢ \: y + 1 = - (5)/(11) (x - 4)}}`

`\large{ \bf{⇢y + 1 = - (5)/(11)x + (20)/(11) }}`

`\large{ \bf{⇢y + 1 = ( - 5x + 20)/(11) }}`

`\large{ \bf{⇢11(y + 1) = - 5x + 20}}`

`\large{ \bf{⇢11y + 11 = - 5x + 20}}`

`\large{ \bf{⇢5x + 11y + 11 - 20 = 0}}`

`⇢ \boxed{\large{ \bold{\bf{5x + 11y - 9 = 0}}}}`

• ♕ Hence , 5x + 11y - 9 = 0 is the required equation of the line.

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