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

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) (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 and .
Also,

is the second point

. So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 5 to both sides.

Combine like terms.

So the equation that goes through the points

and

is

Now simply replace the 'y' with g(x) to get the function

So the function is making the answer d)
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