SOLUTION: What is a function that has the values f(1)=8 and f(7)=-10

Question 254011: What is a function that has the values f(1)=8 and f(7)=-10
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since f(1)=8 and f(7)=-10, this means that the line goes through the points (1,8) and (7,-10)

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 8 to both sides.

Combine like terms.

Simplify

So the equation that goes through the points

and

is

This means that the function is (replace 'y' with f(x))

Notice how the graph of goes through the points

and

. So this visually verifies our answer.

Graph of through the points

and

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