SOLUTION: write an equation for the linear function f satisfying the given conditions 1. f(3)=4 and f(0)=9 2. f(2)=7 and f(8)=1

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Question 68464: write an equation for the linear function f satisfying the given conditions
1. f(3)=4 and f(0)=9
2. f(2)=7 and f(8)=1
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
write an equation for the linear function
f satisfying the given conditions

1. f(3)=4 and f(0)=9 

Use the slope formula:

     f(x2) - f(x1)
m = ———————————————
        x2 - x1

where x1 = 3 and x2 = 0

     (9) - (4)      5       5
m = ——————————— = ———— = - ——— 
     (0) - (3)     -3       3 

Now substitute in the point slope formula:

   f(x) - f(x1) = m(x - x1)

                 5 
f(x) - f(3) = - ———(x - 3)
                 3

                 5 
   f(x) - 4 = - ———(x - 3)
                 3

Distribute to remove the parentheses:

                 5 
   f(x) - 4 = - ———x + 5
                 3

Add 4 to both sides:

                 5 
       f(x) = - ———x + 9
                 3  


2. f(2)=7 and f(8)=1

Use the slope formula:

     f(x2) - f(x1)
m = ———————————————
        x2 - x1

where x1 = 2 and x2 = 8

     (1) - (7)     -6       
m = ——————————— = ———— = -1  
     (8) - (2)      6        

Now substitute in the point slope formula:

   f(x) - f(x1) = m(x - x1)

                  
f(x) - f(2) = -1(x - 2)
                                   
   f(x) - 7 = -1(x - 2)
                 
Distribute to remove the parentheses:

                  
   f(x) - 7 = -x + 2
                 
Add 7 to both sides:
                  
       f(x) = -x + 9
                   
Edwin
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