# 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. 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 $x$ and $y$ axis.
• Remember that the standard function for a linear equation is: $Y=mx+n$
2. 2
Use substitution to begin solving the equation. Substitute the given values of $x$ and $y$ in order to get the values of $m$ and $n$, where $m$ is the slope of the equation and $n$ is the constant of the equation.
• From the table above, the first row says that the value of $x$ is equal to $-6$ and the value of $y$ is $-3$. You therefore write: $-3=m(-6)+(n)$
• The second numbers from the given values are $x=0$ and $y=-1$, so again substitute them into the linear equation: as $-1=m(0)+(n)$, then simplify to: $-1=n$
• You then have: $n=-1$
3. 3
Use subtraction to find the value of $m$ and $n$ 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. 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 $6$, to isolate the $m$ variable.
• You will have:
• Therefore, the value of $m={\frac {1}{3}}$ and $n=-1$.
• Finally, the equation that describes the function table is: $y=-{\frac {1}{3x}}-1$
5. 5
Alternatively, you can use the equation $m={\frac {y2-y1}{x2-x1}}$ to find the equation of the function table.
• From the table above, substitute values of $x$ and $y$ from points 1 (y1=-3;x1=-6) and point 2 (x2=0; y2= -1) into the equation: $m={\frac {y2-y1}{x2-x1}}$.
• Write: $m={\frac {-1-(-3)}{0-(-6)}}$
• Simplify to: $m={\frac {\frac {2}{6}}{\frac {1}{3}}}$
• Now, solve for n using the standard form of equation, where $y$ is = $-3$ and $x=-6$
• Write: $-6=1/3(-3)+n$
• Solve the above problem, finding that: $n=-1$
• The function table's equation is then: $y={\frac {1}{3x}}-1$

## Article Info

Categories: Mathematics