# Find the Function Rule table[[x,y],[0,10],[1,12],[2,14]] 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 .
Simplify each equation.
Simplify .
Multiply by .
Multiply by .
Move to the left of .
Rewrite the equation as .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
Remove parentheses.
Remove parentheses.
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 .
Replace all occurrences of in with .
Simplify .
Multiply by .
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 .
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 .
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