SOLUTION: Write a linear function g given that g(0)=5 and g(10)=9. Answers are multiple choice a. g(x)=5/2x-5 b. g(x)=5/2x+5 c. g(x)=2/5x-5 d. g(x)=2/5x+5 I dont understand how to fi

Algebra ->  Functions -> SOLUTION: Write a linear function g given that g(0)=5 and g(10)=9. Answers are multiple choice a. g(x)=5/2x-5 b. g(x)=5/2x+5 c. g(x)=2/5x-5 d. g(x)=2/5x+5 I dont understand how to fi      Log On


   

Question 275011: Write a linear function g given that g(0)=5 and g(10)=9. Answers are multiple choice
a. g(x)=5/2x-5
b. g(x)=5/2x+5
c. g(x)=2/5x-5
d. g(x)=2/5x+5
I dont understand how to figure out how to get the answer. Thanks for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since g(0)=5 and g(10)=9, we know that the line goes through the points (0,5) and (10,9)


So let's find the equation of the line that goes through the points and


First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=0 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=10 and y%5B2%5D=9.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%289-5%29%2F%2810-0%29 Plug in y%5B2%5D=9, y%5B1%5D=5, x%5B2%5D=10, and x%5B1%5D=0


m=%284%29%2F%2810-0%29 Subtract 5 from 9 to get 4


m=%284%29%2F%2810%29 Subtract 0 from 10 to get 10


m=2%2F5 Reduce


So the slope of the line that goes through the points and is m=2%2F5


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-5=%282%2F5%29%28x-0%29 Plug in m=2%2F5, x%5B1%5D=0, and y%5B1%5D=5


y-5=%282%2F5%29x%2B%282%2F5%29%280%29 Distribute


y-5=%282%2F5%29x%2B0 Multiply


y=%282%2F5%29x%2B0%2B5 Add 5 to both sides.


y=%282%2F5%29x%2B5 Combine like terms.


So the equation that goes through the points and is y=%282%2F5%29x%2B5


Now simply replace the 'y' with g(x) to get the function g%28x%29=%282%2F5%29x%2B5


So the function is g%28x%29=%282%2F5%29x%2B5 making the answer d)