# Linear Algebra Examples

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 the first equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Solve for in the second equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Simplify.

Simplify the right side.

Simplify each term.

Divide by to get .

Multiply by to get .

Add and to get .

Simplify the right side.

Multiply by to get .

Divide by to get .

Subtract from to get .

Solve for in the third equation.

Always true

Remove any equations from the system that are always true.

Calculate the value of using each value in the relation and compare this value to the given value in the relation.

Multiply by to get .

Add and to get .

If the table has a linear function rule, for the corresponding value, . This check passes since and .

Multiply by to get .

Add and to get .

If the table has a linear function rule, for the corresponding value, . This check passes since and .

Multiply by to get .

Add and to get .

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 .

Use the function rule equation to find .

Simplify.