Question

derive an equation of the line passing (x1, y1) and(x2, y2) hance find the equation of the line passing through the point (4, 7) and(-3, 8)​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Points are (4,7) and (-3,8)}$

$\underline{\textsf{To find:}}$

$\textsf{The equation of the line passing through the given points}$

$\underline{\textsf{Solution:}}$

$\textsf{Slope of the line joining points}\mathsf{(x_1,y_1)}\,\textsf{and}\,\mathsf{(x_2,y_2)}$

$\implies\mathsf{m=\dfrac{y_2-y_1}{x_2-x_1}}$

$\textsf{The equation of line passes through}\,\mathsf{(x_1,y_1)}$

$\textsf{having slope m is}$

$\mathsf{y-y_1=m(x-x_1)}$

$\mathsf{y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}$

$\implies\boxed{\mathsf{\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}}}$

$\textsf{which is the required equation of the line}$

$\textsf{The equation of the line joining (4,7) and (-3,8) is}$

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

$\mathsf{\dfrac{y-7}{8-7}=\dfrac{x-4}{-3-4}}$

$\mathsf{\dfrac{y-7}{1}=\dfrac{x-4}{-7}}$

$\mathsf{-7(y-7)=x-4}$

$\mathsf{-7y+49=x-4}$

$\implies\boxed{\mathsf{x+7y-53=0}}$