what line passes through point (-2,3) (1,-6) ?

Question

you must put it in standard form 

 

Answer 1

find the slope:

 

  m =( -6 - 3) / ( 1+ 2) = -3

 

Y = mx + b / slope interest form

                                                   ( 1)

mx - y = -b   / is a standard form

 

Equation of our line L::

 

  - 3 X - y = -b

 

   passes through points ( -2,3) & ( 1, -6)

 

  -3( -2) - 3 = -b

 

   b = -3

 

    then L: -3X - y = 3

 

          then 3X + Y = -3

 

      All forms are equation of the same line, one form can be obtained by moving around the terms of the other, like (1), you don't need to memorize formulas for each form and confuse them. 

 

  

Answer 2

Let (x,y) be another point on the line.

 

Slope, m = (y - 3)/(x- -2) = (-6 - 3)/(1- -2) = -9/3 = -3

 

Multiply both sides by x+2:

 

y - 3 = -3(x+2) = -3x - 6

 

Add 3x + 3 to both sides:

 

3x + y = -3