Question 72826
<pre>

The graph of a function F(x)=mx + b contains the points (5,15) and (-3,-5). Find b.

Formula for slope (m)

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

({{{x[1]}}},{{{y[1]}}}) = (5, 15)

({{{x[2]}}},{{{y[2]}}}) = (-3, -5)

 
            -5 - 15
       m = __________
            -3 - 5

             -20          5
         =  ______ or    ___
             - 8          2

To find the f(x),


        F(x) = mx + b , m = 5/2, (x, y) = (5, 15)

                  15 = (5/2)(5) + b
                  15 = 25/2 + b
           15 - 25/2 = b
         30/2 - 25/2 = b
                 5/2 = b 
          

   F(x) = (5/2)x + 5/2

The graph looks like this

{{{graph (200, 200, -3, 5, -4, 7, (5/2)x + 5/2)}}}