find the equation of the line in standard form that passes through the following points. Simplify your answer. (3, -12) and (-12, 0)

Question

HELP PLEASE

Answer 1

The Standard Format of the equation of a line is:  Ax + By = C

 

You should, once and forever, convert that to the slope-intercept form for the equation of a line and remember that:

    -  the slope is (-A/B)

    -  the y-intercept is (C/B)

 

If both points (3,-12) and (-12,0) are on this line then:

     A(3) + B(-12) = C = A(-12) + B(0)

     3A -12B = -12A

      15A = 12B

          (-A/B) = -4/5    (the slope)

 

The equation has the form:  4x + 5y = C    and we need one of the points to find C  [use (-12,0)]

          4(-12) + 5(0) = C

                -48 = C

 

The equation is:  4x + 5y = -48   (in Standard Format)

 

Check:

  Is  4(3) + 5(-12) = -48   ?

          12 - 60 = -48   ?

                -48 = -48   ?yes

  Is 4(-12) + 5(0) = -48   ?

         -48  = -48   ?yes