# Algebra Examples

Find the Function Rule
Step 1
Check if the function rule is linear.
To find if the table follows a function rule, check to see if the values follow the linear form .
Build a set of equations from the table such that .
Calculate the values of and .
Solve for in .
Rewrite the equation as .
Move to the left of .
Subtract from both sides of the equation.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify the left side.
Remove parentheses.
Simplify the right side.
Simplify .
Move to the left of .
Subtract from .
Replace all occurrences of in with .
Simplify .
Simplify the left side.
Remove parentheses.
Simplify the right side.
Simplify .
Move to the left of .
Subtract from .
Replace all occurrences of in with .
Simplify .
Simplify the left side.
Remove parentheses.
Simplify the right side.
Simplify .
Move to the left of .
Subtract from .
Solve for in .
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Multiply by .
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Multiply by .
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Multiply by .
Subtract from .
Remove any equations from the system that are always true.
List all of the solutions.
Calculate the value of using each value in the relation and compare this value to the given value in the relation.
Calculate the value of when , , and .
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Multiply by .