Question

What is the equation of the line that passes through the points (3, 4) and (5, 7)?

Answer 1

Equation of a line passing through two points is given by

(y-y1)=(y2-y1)/(x2-x1) ×(x-x1)

Answer 2

$\tt \: Equation \: of \: line \: passing \: through \: points \: (x_1 , y_1) \: and \: (x_2 , y_2) :$

$\tt \large \longrightarrow y - y_1 =( x-x_1)\bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg )$

$\tt \large \rightarrow \: here \: \bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg ) is \: slope \: of \: line.$

Now , we have to find out the equation of the line that passes through the points (3, 4) and (5, 7).

$\tt \large \implies y - 4 = (x-3)\bigg( \dfrac{7-4}{ 5-3} \bigg )$

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

$\tt \large \implies 2(y - 4) = 3(x-3)$

$\tt \large \implies 2y - 8 = 3x-9$

$\tt \large \implies 2y -3x = 8-9$

$\tt \large \implies 2y -3x = -1$

$\tt \large \implies 2y -3x+1=0$

Answer :

$\bf \large \implies 2y -3x+1=0$