Question

Find the equation in standard form of the line passing through the points 3,-4 and 5,1

Answer 1

5x - 2y - 23 = 0

Explanation:

Line is passing through the points
`(3,\:-4)= (x_1, \:y_1) \: \&\: (5,\: 1)= (x_2,\:y_2)`

Equation of line in two point form is given as:

`(y -y_1 )/(y_1 -y_2 ) = (x -x_1 )/(x_1 -x_2 ) \\ \\ \therefore \: (y -( - 4) )/( - 4 -1) = (x -3 )/(3 -5 ) \\ \\ \therefore \:(y + 4 )/( - 5) = (x -3 )/( - 2 ) \\ \\ \therefore \: (y + 4 )/( 5) = (x -3 )/( 2 ) \\ \\ \therefore \: 2(y + 4) = 5(x - 3) \\ \therefore \: 2y + 8 = 5x - 15 \\ \therefore \: 5x - 15 - 2y - 8 = 0 \\ \red{ \boxed{ \bold{\therefore \: 5x - 2y - 23 = 0}}} \\ is \: the \: required \: equation \: of \: line \: in \: \\ standard \: form.`