Find the Function Rule table[[x,y],[0,3],[1,4],[2,5]]

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \end{array}$

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 $y = a x + b$ .

$3 = a (0) + b 4 = a (1) + b 5 = a (2) + b$

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

Rewrite the equation as $b = 3$ .

$b = 3$

$4 = a + b$

$5 = a (2) + b$

Replace all occurrences of $b$ with $3$ in each equation.

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

$4 = a + 3$

$b = 3$

$5 = a (2) + b$

Simplify the left side.

Remove parentheses.

$4 = a + 3$

$b = 3$

$5 = a (2) + b$

$4 = a + 3$

$b = 3$

$5 = a (2) + b$

Replace all occurrences of $b$ in $5 = a (2) + b$ with $3$ .

$5 = a (2) + 3$

$4 = a + 3$

$b = 3$

Simplify $5 = a (2) + 3$ .

Simplify the left side.

Remove parentheses.

$5 = a (2) + 3$

$4 = a + 3$

$b = 3$

$5 = a (2) + 3$

$4 = a + 3$

$b = 3$

Simplify the right side.

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

$5 = 2 a + 3$

$4 = a + 3$

$b = 3$

$5 = 2 a + 3$

$4 = a + 3$

$b = 3$

$5 = 2 a + 3$

$4 = a + 3$

$b = 3$

$5 = 2 a + 3$

$4 = a + 3$

$b = 3$

Solve for $a$ in $5 = 2 a + 3$ .

Rewrite the equation as $2 a + 3 = 5$ .

$2 a + 3 = 5$

$4 = a + 3$

$b = 3$

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

Subtract $3$ from both sides of the equation.

$2 a = 5 - 3$

$4 = a + 3$

$b = 3$

Subtract $3$ from $5$ .

$2 a = 2$

$4 = a + 3$

$b = 3$

$2 a = 2$

$4 = a + 3$

$b = 3$

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

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

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

$4 = a + 3$

$b = 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$4 = a + 3$

$b = 3$

Divide $a$ by $1$ .

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

$4 = a + 3$

$b = 3$

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

$4 = a + 3$

$b = 3$

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

$4 = a + 3$

$b = 3$

Simplify the right side.

Divide $2$ by $2$ .

$a = 1$

$4 = a + 3$

$b = 3$

$a = 1$

$4 = a + 3$

$b = 3$

$a = 1$

$4 = a + 3$

$b = 3$

$a = 1$

$4 = a + 3$

$b = 3$

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

Replace all occurrences of $a$ in $4 = a + 3$ with $1$ .

$4 = (1) + 3$

$a = 1$

$b = 3$

Simplify the right side.

Add $1$ and $3$ .

$4 = 4$

$a = 1$

$b = 3$

$4 = 4$

$a = 1$

$b = 3$

$4 = 4$

$a = 1$

$b = 3$

Remove any equations from the system that are always true.

$a = 1$

$b = 3$

List all of the solutions.

$a = 1, b = 3$

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 $a = 1$ , $b = 3$ , and $x = 0$ .

Multiply $0$ by $1$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 0$ . This check passes since $y = 3$ and $y = 3$ .

$3 = 3$

Calculate the value of $y$ when $a = 1$ , $b = 3$ , and $x = 1$ .

Multiply $1$ by $1$ .

$y = 1 + 3$

Add $1$ and $3$ .

$y = 4$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 1$ . This check passes since $y = 4$ and $y = 4$ .

$4 = 4$

Calculate the value of $y$ when $a = 1$ , $b = 3$ , and $x = 2$ .

Multiply $2$ by $1$ .

$y = 2 + 3$

Add $2$ and $3$ .

$y = 5$

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

$5 = 5$

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 $y = x + 3$ .

$y = x + 3$

Find the Function Rule table[[x,y],[0,3],[1,4],[2,5]]

Related Questions

Support LCMGCF.com by disabling your adblocker.