SOLUTION: write an equation in standard form using only integers for each of line described the line through (-2,a) and (a,3) has slope -1/2

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Question 700725: write an equation in standard form using only integers for each of line described
the line through (-2,a) and (a,3) has slope -1/2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We'll need the slope formula first

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

And then we will need point-slope formula:

y - y1 = m(x - x1)

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

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m = %28%283%29-%28a%29%29%2F%28%28a%29-%28-2%29%29

m = %283-a%29%2F%28a%2B2%29

We are give that that equals -1%2F2

%283-a%29%2F%28a%2B2%29 = -1%2F2

%283-a%29%2F%28a%2B2%29 = %28-1%29%2F2

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 - y1 = m(x - x1)

(-2,8)

   y - 8 = -1%2F2%29(x - (-2) )

   y - 8 = -1%2F2%29(x + 2)

Multiply both sides by 2

2(y - 8) = 2×-1%2F2%29(x + 2)

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

 2y - 16 = -x - 2

  x + 2y = 14

Edwin