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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

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

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

Factor $2$ out of $- 4 \cdot - 2$ .

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

Factor $2$ out of $6$ .

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

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

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

Cancel the common factors.

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

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

Factor $2$ out of $2$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Multiply $- 2$ by $- 2$ .

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

Add $4$ and $3$ .

$y = \frac{7}{- (- 1) + 1}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$y = \frac{7}{1 + 1}$

Add $1$ and $1$ .

$y = \frac{7}{2}$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the numerator.

Multiply $- 4$ by $- 1$ .

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

Add $4$ and $6$ .

$y = \frac{10}{- (- 1) + 2}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$y = \frac{10}{1 + 2}$

Add $1$ and $2$ .

$y = \frac{10}{3}$

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

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

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

Factor $2$ out of $- 4 \cdot 0$ .

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

Factor $2$ out of $6$ .

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

Factor $2$ out of $2 (- 2 \cdot 0) + 2 (3)$ .

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

Cancel the common factors.

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

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

Factor $2$ out of $2$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Multiply $- 2$ by $0$ .

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

Add $0$ and $3$ .

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

Simplify the denominator.

Multiply $- 1$ by $0$ .

$y = \frac{3}{0 + 1}$

Add $0$ and $1$ .

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

Divide $3$ by $1$ .

$y = 3$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the numerator.

Multiply $- 4$ by $1$ .

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

Add $- 4$ and $6$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

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

Add $- 1$ and $2$ .

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

Divide $2$ by $1$ .

$y = 2$

Step 9

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

$\begin{array}{c} x & y \\ - 2 & \frac{7}{2} \\ - 1 & \frac{10}{3} \\ 0 & 3 \\ 1 & 2 \end{array}$

Step 10

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

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