Write an equation in standard form for a line that passes through (2,2) and (0,-3)

Question

Ok so this question is telling me to write an equation in standard form for a line that passes through (2,2) and (0,-3)

Answer 1

The Standard Form of the equation of a line is Ax+By=C.

 

The problem gives two points which are on this line -->   (2,2) and (0,-3).

      A(2)+B(2)  =C

      A(0)+B(-3) =C

    -------------------    [subtract equations]

       2A  + 5B    = 0

      2A = -5B              [choose A=5, B=-2]

 

The equation is:    5x - 2y = C         [use either point to find C]

       5(0) - 2(-3) = C

               6 = C

 

In Standard Format, the equation is:    5x -2y = 6

 

Check:

    Is   5(2) -2(2) = 6   ?

           10-4 = 6   ?

              6 = 6   >yes

    Is 5(0) -2(-3) = 6   ?

                6 = 6   ?yes

Answer 2

HOW TO SOLVE:

1. Calculate m, using the two points given.

2. choose one of the given points and substitute those coordinates, and m, into the POINT SLOPE form

   y - y₁ = m(x - x₁₎

3. Clean up the equation & present answer in Standard Form or Slope Intercept form, whichever is preferred or requested.

 

this is very doable & this type of thing occurs over and over in mathematics, so learn & remember!