Graph Using a Table of Values 2x-3y=12

$2 x - 3 y = 12$

Step 1

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

$2 (- 2) - 3 y = 12$

Step 2

Solve the equation for $y$ .

Multiply $2$ by $- 2$ .

$- 4 - 3 y = 12$

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

Add $4$ to both sides of the equation.

$- 3 y = 12 + 4$

Add $12$ and $4$ .

$- 3 y = 16$

Divide each term in $- 3 y = 16$ by $- 3$ and simplify.

Divide each term in $- 3 y = 16$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{16}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{16}{- 3}$

Divide $y$ by $1$ .

$y = \frac{16}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{16}{3}$

Step 3

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

$2 (- 1) - 3 y = 12$

Step 4

Solve the equation for $y$ .

Multiply $2$ by $- 1$ .

$- 2 - 3 y = 12$

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

Add $2$ to both sides of the equation.

$- 3 y = 12 + 2$

Add $12$ and $2$ .

$- 3 y = 14$

Divide each term in $- 3 y = 14$ by $- 3$ and simplify.

Divide each term in $- 3 y = 14$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{14}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{14}{- 3}$

Divide $y$ by $1$ .

$y = \frac{14}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{14}{3}$

Step 5

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

$2 (0) - 3 y = 12$

Step 6

Solve the equation for $y$ .

Simplify $2 (0) - 3 y$ .

Multiply $2$ by $0$ .

$0 - 3 y = 12$

Subtract $3 y$ from $0$ .

$- 3 y = 12$

Divide each term in $- 3 y = 12$ by $- 3$ and simplify.

Divide each term in $- 3 y = 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

Divide $y$ by $1$ .

$y = \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$y = - 4$

Step 7

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

$2 (1) - 3 y = 12$

Step 8

Solve the equation for $y$ .

Multiply $2$ by $1$ .

$2 - 3 y = 12$

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

Subtract $2$ from both sides of the equation.

$- 3 y = 12 - 2$

Subtract $2$ from $12$ .

$- 3 y = 10$

Divide each term in $- 3 y = 10$ by $- 3$ and simplify.

Divide each term in $- 3 y = 10$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 9

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

$2 (2) - 3 y = 12$

Step 10

Solve the equation for $y$ .

Multiply $2$ by $2$ .

$4 - 3 y = 12$

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

Subtract $4$ from both sides of the equation.

$- 3 y = 12 - 4$

Subtract $4$ from $12$ .

$- 3 y = 8$

Divide each term in $- 3 y = 8$ by $- 3$ and simplify.

Divide each term in $- 3 y = 8$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{8}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{8}{- 3}$

Divide $y$ by $1$ .

$y = \frac{8}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{16}{3} \\ - 1 & - \frac{14}{3} \\ 0 & - 4 \\ 1 & - \frac{10}{3} \\ 2 & - \frac{8}{3} \end{array}$

Step 12

Graph Using a Table of Values 2x-3y=12

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