Question 700725
<pre>
We'll need the slope formula first

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}

And then we will need point-slope formula:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

(-2,a) and (a,3) has slope -1/2

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}

m = {{{((3)-(a))/((a)-(-2))}}}

m = {{{(3-a)/(a+2)}}}

We are give that that equals {{{-1/2}}}

{{{(3-a)/(a+2)}}} = {{{-1/2}}}

{{{(3-a)/(a+2)}}} = {{{(-1)/2}}}

Cross multiply:

2(3-a) = -1(a+2)

  6-2a = -a-2
    -a = -8
     a = 8

So the points 

(-2,a) and (a,3) become the points

(-2,8) and (8,3) 

Using the point-slope form:

  y - y<sub>1</sub> = m(x - x<sub>1</sub>)

(-2,8)

   y - 8 = {{{-1/2)}}}(x - (-2) )

   y - 8 = {{{-1/2)}}}(x + 2)

Multiply both sides by 2

2(y - 8) = 2×{{{-1/2)}}}(x + 2)

 2y - 16 = -1(x + 2)

 2y - 16 = -x - 2

  x + 2y = 14

Edwin</pre>