Question 73870
<pre>
Write the equaition of the line through the points (-5,-7) and (-6,-4).

A)  12; y=11*x+69

B)  11; y=12*x+68

C)  11; y=11*x+69

D)  12; y=12*x+68




You can solve this in two ways

       Slope - intercept Formula 

            y = mx + b, where m = slope and b = y- intercept

      Formula for the Slope (m)

                {{{y[2]-y[1]}}}
            m = ___________
                {{{x[2]-x[1]}}}

 Given two point , we solve for the slope

  (-5,-7) = ({{{x[1]}}},{{{y[1]}}})
  (-6,-4) = ({{{x[2]}}},{{{y[2]}}})

Substitute to the formula of the slope

                 -4 - (-7)
            m = ___________
                 -6 - (-5)


                 -4 + 7
            m = ___________
                 -6 + 5


                    3
            m = ___________ or -3
                   -1

Then solve for b (y - intercept) by using the formula slope-intercept form
(x,y) = (-5,-7) or (-6,-4), m = -3
we use (-5, -7) for (x,y)

                 y = mx + b
                -7 = -3(-5) + b
                -7 = 15 + b
           -7 - 15 = 15 - 15 + b
               -22 = b

Now we have m = -3 and b = -22

      Equation of the line

             y = mx + b
             y = -3x - 22


Equation of the line in standard form

            y = -3x - 22
           3x + y + 22 = 0

Note i don't know why the answer is not in the choices.