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 $y$ .

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

Step 2

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

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

Factor $2$ out of $4 (- 2)$ .

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

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 $- 2$ .

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

Subtract $3$ from $- 4$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

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

Add $1$ and $1$ .

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

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

Simplify the numerator.

Multiply $4$ by $- 1$ .

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

Subtract $6$ from $- 4$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

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

Add $1$ and $2$ .

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

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

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

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

Factor $2$ out of $4 (0)$ .

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

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 $0$ .

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

Subtract $3$ from $0$ .

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

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 $y$ .

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the numerator.

Multiply $4$ by $1$ .

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

Subtract $6$ from $4$ .

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

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)

Related Questions

Support LCMGCF.com by disabling your adblocker.