Find the Function Rule table[[x,y],[-1,7],[0,4],[1,1]]

$\begin{array}{c} x & y \\ - 1 & 7 \\ 0 & 4 \\ 1 & 1 \end{array}$

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 $y = a x + b$ .

$7 = a (- 1) + b 4 = a (0) + b 1 = a (1) + b$

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

Rewrite the equation as $b = 4$ .

$b = 4$

$7 = a (- 1) + b$

$1 = a + b$

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

Replace all occurrences of $b$ in $7 = a (- 1) + b$ with $4$ .

$7 = a (- 1) + 4$

$b = 4$

$1 = a + b$

Simplify $7 = a (- 1) + 4$ .

Simplify the left side.

Remove parentheses.

$7 = a (- 1) + 4$

$b = 4$

$1 = a + b$

$7 = a (- 1) + 4$

$b = 4$

$1 = a + b$

Simplify the right side.

Simplify each term.

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

$7 = - 1 a + 4$

$b = 4$

$1 = a + b$

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

$7 = - a + 4$

$b = 4$

$1 = a + b$

$7 = - a + 4$

$b = 4$

$1 = a + b$

$7 = - a + 4$

$b = 4$

$1 = a + b$

$7 = - a + 4$

$b = 4$

$1 = a + b$

Replace all occurrences of $b$ in $1 = a + b$ with $4$ .

$1 = a + 4$

$7 = - a + 4$

$b = 4$

Simplify the left side.

Remove parentheses.

$1 = a + 4$

$7 = - a + 4$

$b = 4$

$1 = a + 4$

$7 = - a + 4$

$b = 4$

$1 = a + 4$

$7 = - a + 4$

$b = 4$

Solve for $a$ in $1 = a + 4$ .

Rewrite the equation as $a + 4 = 1$ .

$a + 4 = 1$

$7 = - a + 4$

$b = 4$

Move all terms not containing $a$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$a = 1 - 4$

$7 = - a + 4$

$b = 4$

Subtract $4$ from $1$ .

$a = - 3$

$7 = - a + 4$

$b = 4$

$a = - 3$

$7 = - a + 4$

$b = 4$

$a = - 3$

$7 = - a + 4$

$b = 4$

Replace all occurrences of $a$ with $- 3$ in each equation.

Replace all occurrences of $a$ in $7 = - a + 4$ with $- 3$ .

$7 = - (- 3) + 4$

$a = - 3$

$b = 4$

Simplify the right side.

Simplify $- (- 3) + 4$ .

Multiply $- 1$ by $- 3$ .

$7 = 3 + 4$

$a = - 3$

$b = 4$

Add $3$ and $4$ .

$7 = 7$

$a = - 3$

$b = 4$

$7 = 7$

$a = - 3$

$b = 4$

$7 = 7$

$a = - 3$

$b = 4$

$7 = 7$

$a = - 3$

$b = 4$

Remove any equations from the system that are always true.

$a = - 3$

$b = 4$

List all of the solutions.

$a = - 3, b = 4$

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 $a = - 3$ , $b = 4$ , and $x = - 1$ .

Multiply $- 3$ by $- 1$ .

$y = 3 + 4$

Add $3$ and $4$ .

$y = 7$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = - 1$ . This check passes since $y = 7$ and $y = 7$ .

$7 = 7$

Calculate the value of $y$ when $a = - 3$ , $b = 4$ , and $x = 0$ .

Multiply $- 3$ 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 $a = - 3$ , $b = 4$ , and $x = 1$ .

Multiply $- 3$ by $1$ .

$y = - 3 + 4$

Add $- 3$ and $4$ .

$y = 1$

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

$1 = 1$

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 $y = - 3 x + 4$ .

$y = - 3 x + 4$

Find the Function Rule table[[x,y],[-1,7],[0,4],[1,1]]

Related Questions

Support LCMGCF.com by disabling your adblocker.