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 .

Simplify each equation.

Multiply by .

Move to the left of .

Move to the left of .

Solve for in the first equation.

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 .

Replace all occurrences of in with .

Simplify each equation.

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Multiply by .

Add and .

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Multiply by .

Add and .

Solve for in the second equation.

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 by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Dividing two negative values results in a positive value.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Simplify .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Simplify .

Simplify each term.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Subtract from .

Since , the equation will always be true.

Always true

Remove any equations from the system that are always true.

List the solutions to the system of equations.

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 .

Combine the numerators over the common denominator.

Add and .

Divide 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 .

Combine and .

Multiply by .

Combine the numerators over the common denominator.

Add and .

Divide 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 .

Combine and .

Multiply by .

Combine the numerators over the common denominator.

Add and .

Divide 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 .

Find the Function Rule table[[x,y],[1,5],[5,10],[9,15]]