Find the Function Rule table[[x,y],[0,4],[-1,6],[2,0]]

$\begin{array}{c} x & y \\ 0 & 4 \\ - 1 & 6 \\ 2 & 0 \end{array}$

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 $y = a x + b$ .

$y = a x + b$

Build a set of equations from the table such that $y = a x + b$ .

$4 = a (0) + b 6 = a (- 1) + b 0 = a (2) + b$

Calculate the values of $a$ and $b$ .

Rewrite the equation as $b = 4$ .

$b = 4$

$6 = a (- 1) + b$

$0 = a (2) + b$

Replace all occurrences of $b$ with $4$ in each equation.

Replace all occurrences of $b$ in $6 = a (- 1) + b$ with $4$ .

$6 = a (- 1) + 4$

$b = 4$

$0 = a (2) + b$

Simplify $6 = a (- 1) + 4$ .

Simplify the left side.

Remove parentheses.

$6 = a (- 1) + 4$

$b = 4$

$0 = a (2) + b$

$6 = a (- 1) + 4$

$b = 4$

$0 = a (2) + b$

Simplify the right side.

Simplify each term.

Move $- 1$ to the left of $a$ .

$6 = - 1 a + 4$

$b = 4$

$0 = a (2) + b$

Rewrite $- 1 a$ as $- a$ .

$6 = - a + 4$

$b = 4$

$0 = a (2) + b$

$6 = - a + 4$

$b = 4$

$0 = a (2) + b$

$6 = - a + 4$

$b = 4$

$0 = a (2) + b$

$6 = - a + 4$

$b = 4$

$0 = a (2) + b$

Replace all occurrences of $b$ in $0 = a (2) + b$ with $4$ .

$0 = a (2) + 4$

$6 = - a + 4$

$b = 4$

Simplify $0 = a (2) + 4$ .

Simplify the left side.

Remove parentheses.

$0 = a (2) + 4$

$6 = - a + 4$

$b = 4$

$0 = a (2) + 4$

$6 = - a + 4$

$b = 4$

Simplify the right side.

Move $2$ to the left of $a$ .

$0 = 2 a + 4$

$6 = - a + 4$

$b = 4$

$0 = 2 a + 4$

$6 = - a + 4$

$b = 4$

$0 = 2 a + 4$

$6 = - a + 4$

$b = 4$

$0 = 2 a + 4$

$6 = - a + 4$

$b = 4$

Solve for $a$ in $0 = 2 a + 4$ .

Rewrite the equation as $2 a + 4 = 0$ .

$2 a + 4 = 0$

$6 = - a + 4$

$b = 4$

Subtract $4$ from both sides of the equation.

$2 a = - 4$

$6 = - a + 4$

$b = 4$

Divide each term in $2 a = - 4$ by $2$ and simplify.

Divide each term in $2 a = - 4$ by $2$ .

$\frac{2 a}{2} = \frac{- 4}{2}$

$6 = - a + 4$

$b = 4$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{- 4}{2}$

$6 = - a + 4$

$b = 4$

Divide $a$ by $1$ .

$a = \frac{- 4}{2}$

$6 = - a + 4$

$b = 4$

$a = \frac{- 4}{2}$

$6 = - a + 4$

$b = 4$

$a = \frac{- 4}{2}$

$6 = - a + 4$

$b = 4$

Simplify the right side.

Divide $- 4$ by $2$ .

$a = - 2$

$6 = - a + 4$

$b = 4$

$a = - 2$

$6 = - a + 4$

$b = 4$

$a = - 2$

$6 = - a + 4$

$b = 4$

$a = - 2$

$6 = - a + 4$

$b = 4$

Replace all occurrences of $a$ with $- 2$ in each equation.

Replace all occurrences of $a$ in $6 = - a + 4$ with $- 2$ .

$6 = - (- 2) + 4$

$a = - 2$

$b = 4$

Simplify the right side.

Simplify $- (- 2) + 4$ .

Multiply $- 1$ by $- 2$ .

$6 = 2 + 4$

$a = - 2$

$b = 4$

Add $2$ and $4$ .

$6 = 6$

$a = - 2$

$b = 4$

$6 = 6$

$a = - 2$

$b = 4$

$6 = 6$

$a = - 2$

$b = 4$

$6 = 6$

$a = - 2$

$b = 4$

Remove any equations from the system that are always true.

$a = - 2$

$b = 4$

List all of the solutions.

$a = - 2, b = 4$

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

Calculate the value of $y$ when $a = - 2$ , $b = 4$ , and $x = 0$ .

Multiply $- 2$ by $0$ .

$y = 0 + 4$

Add $0$ and $4$ .

$y = 4$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 0$ . This check passes since $y = 4$ and $y = 4$ .

$4 = 4$

Calculate the value of $y$ when $a = - 2$ , $b = 4$ , and $x = - 1$ .

Multiply $- 2$ by $- 1$ .

$y = 2 + 4$

Add $2$ and $4$ .

$y = 6$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = - 1$ . This check passes since $y = 6$ and $y = 6$ .

$6 = 6$

Calculate the value of $y$ when $a = - 2$ , $b = 4$ , and $x = 2$ .

Multiply $- 2$ by $2$ .

$y = - 4 + 4$

Add $- 4$ and $4$ .

$y = 0$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check passes since $y = 0$ and $y = 0$ .

$0 = 0$

Since $y = y$ for the corresponding $x$ values, the function is linear.

The function is linear

Step 2

Since all $y = y$ , the function is linear and follows the form $y = - 2 x + 4$ .

$y = - 2 x + 4$

Find the Function Rule table[[x,y],[0,4],[-1,6],[2,0]]

Related Questions

Support LCMGCF.com by disabling your adblocker.