SOLUTION: Write an equation for each function in the form f(x)= mx+b. 16. f(3)=9, f(5)=15 17. f(-2)=4, f(2)=-16 18. f(0)=5, f(-5)=10 19. f(10)=4, m=1/2

Algebra ->  Algebra  -> Functions -> SOLUTION: Write an equation for each function in the form f(x)= mx+b. 16. f(3)=9, f(5)=15 17. f(-2)=4, f(2)=-16 18. f(0)=5, f(-5)=10 19. f(10)=4, m=1/2      Log On

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Question 54138This question is from textbook Integrated Mathematics 3
: Write an equation for each function in the form f(x)= mx+b.
16. f(3)=9, f(5)=15
17. f(-2)=4, f(2)=-16
18. f(0)=5, f(-5)=10
19. f(10)=4, m=1/2This question is from textbook Integrated Mathematics 3

Answer by tiffanyc(9) About Me  (Show Source):
You can put this solution on YOUR website!
16. f(3)=9, f(5)=15
When x=3 y (or f(x))=9 so plug it into the formula
9=m3+b and 15=m5+b
Use linear algebra to isolate 1 variable:
b=9-m3, and substitute that value of b into the second equation:
15=m5+(9-m3). Now combine your like terms to get 15=m2+9 and then 6=m2
divide both sides by 2 to get m=3 and plug that value into either equation to get the value to b:
9=(3)(3) +b so 9=9+b so b equals 0. Check this with the other equation:
15=(5)(3)+b so 15=15 +0. the equation becomes:
f(x)=3x +0 or simply f(x)=3x