Graph Using a Table of Values f(x)=(2x+6)/(x+4)

$f (x) = \frac{2 x + 6}{x + 4}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \frac{2 (- 2) + 6}{(- 2) + 4}$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{2 (- 2) + 6}{- 2 + 4}$

Remove parentheses.

$y = \frac{2 (- 2) + 6}{(- 2) + 4}$

Simplify $\frac{2 (- 2) + 6}{(- 2) + 4}$ .

Cancel the common factor of $2 (- 2) + 6$ and $(- 2) + 4$ .

Factor $2$ out of $6$ .

$y = \frac{2 (- 2) + 2 (3)}{(- 2) + 4}$

Factor $2$ out of $2 (- 2) + 2 (3)$ .

$y = \frac{2 (- 2 + 3)}{(- 2) + 4}$

Cancel the common factors.

Factor $2$ out of $- 2$ .

$y = \frac{2 (- 2 + 3)}{2 (- 1) + 4}$

Factor $2$ out of $4$ .

$y = \frac{2 (- 2 + 3)}{2 \cdot - 1 + 2 \cdot 2}$

Factor $2$ out of $2 \cdot - 1 + 2 \cdot 2$ .

$y = \frac{2 (- 2 + 3)}{2 \cdot (- 1 + 2)}$

Cancel the common factor.

$y = \frac{2 (- 2 + 3)}{2 \cdot (- 1 + 2)}$

Rewrite the expression.

$y = \frac{- 2 + 3}{- 1 + 2}$

Simplify the expression.

Add $- 2$ and $3$ .

$y = \frac{1}{- 1 + 2}$

Add $- 1$ and $2$ .

$y = \frac{1}{1}$

Divide $1$ by $1$ .

$y = 1$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{2 (- 1) + 6}{(- 1) + 4}$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{2 (- 1) + 6}{- 1 + 4}$

Remove parentheses.

$y = \frac{2 (- 1) + 6}{(- 1) + 4}$

Simplify $\frac{2 (- 1) + 6}{(- 1) + 4}$ .

Simplify the numerator.

Multiply $2$ by $- 1$ .

$y = \frac{- 2 + 6}{- 1 + 4}$

Add $- 2$ and $6$ .

$y = \frac{4}{- 1 + 4}$

Add $- 1$ and $4$ .

$y = \frac{4}{3}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{2 (0) + 6}{(0) + 4}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{2 (0) + 6}{0 + 4}$

Remove parentheses.

$y = \frac{2 (0) + 6}{(0) + 4}$

Simplify $\frac{2 (0) + 6}{(0) + 4}$ .

Cancel the common factor of $2 (0) + 6$ and $(0) + 4$ .

Factor $- 1$ out of $2 (0)$ .

$y = \frac{- (- 2 \cdot 0) + 6}{(0) + 4}$

Rewrite $6$ as $- 1 (- 6)$ .

$y = \frac{- (- 2 \cdot 0) - 1 (- 6)}{(0) + 4}$

Factor $- 1$ out of $- (- 2 \cdot 0) - 1 (- 6)$ .

$y = \frac{- (- 2 \cdot 0 - 6)}{(0) + 4}$

Rewrite $- (- 2 \cdot 0 - 6)$ as $- 1 (- 2 \cdot 0 - 6)$ .

$y = \frac{- 1 (- 2 \cdot 0 - 6)}{(0) + 4}$

Reorder terms.

$y = \frac{- 1 (- 6 - 2 \cdot 0)}{0 + 4}$

Factor $2$ out of $- 1 (- 6 - 2 \cdot 0)$ .

$y = \frac{2 (- 1 (- 3 - 0))}{0 + 4}$

Cancel the common factors.

Factor $2$ out of $0$ .

$y = \frac{2 (- 1 (- 3 - 0))}{2 (0) + 4}$

Factor $2$ out of $4$ .

$y = \frac{2 (- 1 (- 3 - 0))}{2 \cdot 0 + 2 \cdot 2}$

Factor $2$ out of $2 \cdot 0 + 2 \cdot 2$ .

$y = \frac{2 (- 1 (- 3 - 0))}{2 \cdot (0 + 2)}$

Cancel the common factor.

$y = \frac{2 (- 1 (- 3 - 0))}{2 \cdot (0 + 2)}$

Rewrite the expression.

$y = \frac{- 1 (- 3 - 0)}{0 + 2}$

Simplify the numerator.

Multiply $- 1$ by $0$ .

$y = \frac{- 1 (- 3 + 0)}{0 + 2}$

Add $- 3$ and $0$ .

$y = \frac{- 1 \cdot - 3}{0 + 2}$

Simplify the expression.

Add $0$ and $2$ .

$y = \frac{- 1 \cdot - 3}{2}$

Multiply $- 1$ by $- 3$ .

$y = \frac{3}{2}$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{2 (1) + 6}{(1) + 4}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{2 (1) + 6}{1 + 4}$

Remove parentheses.

$y = \frac{2 (1) + 6}{(1) + 4}$

Simplify $\frac{2 (1) + 6}{(1) + 4}$ .

Simplify the numerator.

Multiply $2$ by $1$ .

$y = \frac{2 + 6}{1 + 4}$

Add $2$ and $6$ .

$y = \frac{8}{1 + 4}$

Add $1$ and $4$ .

$y = \frac{8}{5}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{2 (2) + 6}{(2) + 4}$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{2 (2) + 6}{2 + 4}$

Remove parentheses.

$y = \frac{2 (2) + 6}{(2) + 4}$

Simplify $\frac{2 (2) + 6}{(2) + 4}$ .

Cancel the common factor of $2 (2) + 6$ and $(2) + 4$ .

Factor $2$ out of $6$ .

$y = \frac{2 (2) + 2 \cdot 3}{2 + 4}$

Factor $2$ out of $2 (2) + 2 (3)$ .

$y = \frac{2 (2 + 3)}{(2) + 4}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (2 + 3)}{2 (1) + 4}$

Factor $2$ out of $4$ .

$y = \frac{2 (2 + 3)}{2 \cdot 1 + 2 \cdot 2}$

Factor $2$ out of $2 \cdot 1 + 2 \cdot 2$ .

$y = \frac{2 (2 + 3)}{2 \cdot (1 + 2)}$

Cancel the common factor.

$y = \frac{2 (2 + 3)}{2 \cdot (1 + 2)}$

Rewrite the expression.

$y = \frac{2 + 3}{1 + 2}$

Simplify by adding numbers.

Add $2$ and $3$ .

$y = \frac{5}{1 + 2}$

Add $1$ and $2$ .

$y = \frac{5}{3}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 1 \\ - 1 & \frac{4}{3} \\ 0 & \frac{3}{2} \\ 1 & \frac{8}{5} \\ 2 & \frac{5}{3} \end{array}$

Step 12

Graph Using a Table of Values f(x)=(2x+6)/(x+4)

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