Question

What is the equation of the line that passes through (5;-2) and (-3;4

Answer 1

Explanation:

Given points are:
`(5, - 2) =(x_1,\:y_1) \:\&\: (-3, 4)=(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 -( -2 ) )/( - 2 - 4) = (x -5 )/(5 - ( - 3)) \\ \\\therefore \: (y + 2 )/( - 6) = (x -5 )/(5 + 3) \\ \\\therefore \: (y + 2 )/( - 6) = (x -5 )/(8) \\ \\\therefore \: (y + 2 )/( - 3) = (x -5 )/(4) \\ \\\therefore \: 4(y + 2 ) = - 3(x - 5) \\ \\ \therefore \: 4y + 8 = - 3x + 15 \\ \\ \therefore \: 3x + 4y + 8 - 15 = 0 \\ \\ \huge \: \orange{ \boxed{\therefore \: 3x + 4y - 7 = 0}} \\ \: \: is \: the \: required \: equation \: of \: line`