SOLUTION: I was confused on how you solve this question. The question states: write an equation for the linear function f with the given values. f(6)=-4, f(9)=-9

Question 822037: I was confused on how you solve this question. The question states: write an equation for the linear function f with the given values. f(6)=-4, f(9)=-9
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You know equations representing a line that can be written as
with some constants and .
You can think of those equations as linear functions with being a function of .
You could write them as .
That is the type of equation you need to find.
There's more than one way to the answer.
You could substitute the values given and solve the resulting system of equations for and .
You could also draw on what you know of equations of a line,
figure out the slope,
use one point to write the equation in point-slope form,
and then solve for to get the slope-intercept form of the equation.

SOLVING A SYSTEM:
We substitute and into to get two equations.

Subtracting the first equation from the second, we get
--> -->
Substituting that value for into the first equation, we get
--> --> -->
So the linear function is

FINDING THE EQUATION OF A LINE:
The information given, tells you that
for , so point (6,-4) is on the line,
and it also tells you that
for , so point (9,-9) is on the line.
The slope is the difference in values divided by the difference in values:

With that slope and knowing that the line goes through (6,-4) we can write a point-slope form of the equation as
-->
We can solve for --> --> --> -->
Then you would write it with instead of , as

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