Find the Function Rule table[[x,y],[0,1],[2,5],[4,9]]

$\begin{array}{c} x & y \\ 0 & 1 \\ 2 & 5 \\ 4 & 9 \end{array}$

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 $y = a x + b$ .

$1 = a (0) + b 5 = a (2) + b 9 = a (4) + b$

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

Rewrite the equation as $b = 1$ .

$b = 1$

$5 = a (2) + b$

$9 = a (4) + b$

Replace all occurrences of $b$ with $1$ in each equation.

Replace all occurrences of $b$ in $5 = a (2) + b$ with $1$ .

$5 = a (2) + 1$

$b = 1$

$9 = a (4) + b$

Simplify $5 = a (2) + 1$ .

Simplify the left side.

Remove parentheses.

$5 = a (2) + 1$

$b = 1$

$9 = a (4) + b$

$5 = a (2) + 1$

$b = 1$

$9 = a (4) + b$

Simplify the right side.

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

$5 = 2 a + 1$

$b = 1$

$9 = a (4) + b$

$5 = 2 a + 1$

$b = 1$

$9 = a (4) + b$

$5 = 2 a + 1$

$b = 1$

$9 = a (4) + b$

Replace all occurrences of $b$ in $9 = a (4) + b$ with $1$ .

$9 = a (4) + 1$

$5 = 2 a + 1$

$b = 1$

Simplify $9 = a (4) + 1$ .

Simplify the left side.

Remove parentheses.

$9 = a (4) + 1$

$5 = 2 a + 1$

$b = 1$

$9 = a (4) + 1$

$5 = 2 a + 1$

$b = 1$

Simplify the right side.

Move $4$ to the left of $a$ .

$9 = 4 a + 1$

$5 = 2 a + 1$

$b = 1$

$9 = 4 a + 1$

$5 = 2 a + 1$

$b = 1$

$9 = 4 a + 1$

$5 = 2 a + 1$

$b = 1$

$9 = 4 a + 1$

$5 = 2 a + 1$

$b = 1$

Solve for $a$ in $9 = 4 a + 1$ .

Rewrite the equation as $4 a + 1 = 9$ .

$4 a + 1 = 9$

$5 = 2 a + 1$

$b = 1$

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

Subtract $1$ from both sides of the equation.

$4 a = 9 - 1$

$5 = 2 a + 1$

$b = 1$

Subtract $1$ from $9$ .

$4 a = 8$

$5 = 2 a + 1$

$b = 1$

$4 a = 8$

$5 = 2 a + 1$

$b = 1$

Divide each term in $4 a = 8$ by $4$ and simplify.

Divide each term in $4 a = 8$ by $4$ .

$\frac{4 a}{4} = \frac{8}{4}$

$5 = 2 a + 1$

$b = 1$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a}{4} = \frac{8}{4}$

$5 = 2 a + 1$

$b = 1$

Divide $a$ by $1$ .

$a = \frac{8}{4}$

$5 = 2 a + 1$

$b = 1$

$a = \frac{8}{4}$

$5 = 2 a + 1$

$b = 1$

$a = \frac{8}{4}$

$5 = 2 a + 1$

$b = 1$

Simplify the right side.

Divide $8$ by $4$ .

$a = 2$

$5 = 2 a + 1$

$b = 1$

$a = 2$

$5 = 2 a + 1$

$b = 1$

$a = 2$

$5 = 2 a + 1$

$b = 1$

$a = 2$

$5 = 2 a + 1$

$b = 1$

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

Replace all occurrences of $a$ in $5 = 2 a + 1$ with $2$ .

$5 = 2 (2) + 1$

$a = 2$

$b = 1$

Simplify the right side.

Simplify $2 (2) + 1$ .

Multiply $2$ by $2$ .

$5 = 4 + 1$

$a = 2$

$b = 1$

Add $4$ and $1$ .

$5 = 5$

$a = 2$

$b = 1$

$5 = 5$

$a = 2$

$b = 1$

$5 = 5$

$a = 2$

$b = 1$

$5 = 5$

$a = 2$

$b = 1$

Remove any equations from the system that are always true.

$a = 2$

$b = 1$

List all of the solutions.

$a = 2, b = 1$

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 $a = 2$ , $b = 1$ , and $x = 0$ .

Multiply $2$ by $0$ .

$y = 0 + 1$

Add $0$ and $1$ .

$y = 1$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 0$ . This check passes since $y = 1$ and $y = 1$ .

$1 = 1$

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

Multiply $2$ by $2$ .

$y = 4 + 1$

Add $4$ and $1$ .

$y = 5$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check passes since $y = 5$ and $y = 5$ .

$5 = 5$

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

Multiply $2$ by $4$ .

$y = 8 + 1$

Add $8$ and $1$ .

$y = 9$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 4$ . This check passes since $y = 9$ and $y = 9$ .

$9 = 9$

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 $y = 2 x + 1$ .

$y = 2 x + 1$

Find the Function Rule table[[x,y],[0,1],[2,5],[4,9]]

Related Questions

Support LCMGCF.com by disabling your adblocker.