# How to Create an Equation from a Function Table

A function table is a table of ordered pairs that follows a rule defining how one number relates to the other, in a pattern. Additionally, because they are ordered pairs of a linear line, they also act as coordinates for points that the line intersects, and are governed by a shared linear equation. You can create an equation from a function table, in order to determine its linear line.

## Steps

- 1
**Take a look at the example function table to begin solving for the equation.**Below:- In the above table, the coordinates of the line are the and axis.
- Remember that the standard function for a linear equation is:

- 2
**Use substitution to begin solving the equation.**Substitute the given values of and in order to get the values of and , where is the slope of the equation and is the constant of the equation.- From the table above, the first row says that the value of is equal to and the value of is . You therefore write:
- The second numbers from the given values are and , so again substitute them into the linear equation: as , then simplify to:
- You then have:

- 3
**Use subtraction to find the value of and in the equation.**- Take note of the fact that negative sign outside of the parentheses changes the the signs of each term differently, when multiplied to the equation inside the parentheses.
- Remember, multiplication of like signs turns the equation positive and multiplication of unlike signs turns the equation negative. Therefore, you write the equation as:

- 4
**Continue the operation with addition.**Now, add the positive values of both negative terms to each side to get positive terms on each side.- You will then have:
- Divide both sides by , to isolate the variable.
- You will have:
- Therefore, the value of and .
- Finally, the equation that describes the function table is:

- 5
**Alternatively, you can use the equation to find the equation of the function table.**- From the table above, substitute values of and from points 1 (y1=-3;x1=-6) and point 2 (x2=0; y2= -1) into the equation: .
- Write:
- Simplify to:
- Now, solve for n using the standard form of equation, where is = and
- Write:
- Solve the above problem, finding that:
- The function table's equation is then:

## Article Info

Categories: Mathematics