# Algebra Examples

Step 1
Find the function rule.
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 .
Subtract from both sides of the equation.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Solve for in .
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
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 .
Replace all occurrences of in with .
Simplify the right side.
Subtract from .
Replace all occurrences of in with .
Simplify the right side.
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 .
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 .
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 .
Since for the corresponding values, the function is linear.
The function is linear
The function is linear
The function is linear
Since all , the function is linear and follows the form .
Step 2
Find .
Use the function rule equation to find .
Simplify.
Step 3
Find .
Use the function rule equation to find .
Simplify.
Step 4
List all of the solutions.