Graph Using a Table of Values 2x-3y=-6

$2 x - 3 y = - 6$

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

$2 (- 2) - 3 y = - 6$

Solve the equation for $y$ .

Multiply $2$ by $- 2$ .

$- 4 - 3 y = - 6$

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

Add $4$ to both sides of the equation.

$- 3 y = - 6 + 4$

Add $- 6$ and $4$ .

$- 3 y = - 2$

Divide each term in $- 3 y = - 2$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 2$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

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

$2 (- 1) - 3 y = - 6$

Solve the equation for $y$ .

Multiply $2$ by $- 1$ .

$- 2 - 3 y = - 6$

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

Add $2$ to both sides of the equation.

$- 3 y = - 6 + 2$

Add $- 6$ and $2$ .

$- 3 y = - 4$

Divide each term in $- 3 y = - 4$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 4$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

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

$2 (0) - 3 y = - 6$

Solve the equation for $y$ .

Simplify $2 (0) - 3 y$ .

Multiply $2$ by $0$ .

$0 - 3 y = - 6$

Subtract $3 y$ from $0$ .

$- 3 y = - 6$

Divide each term in $- 3 y = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$y = 2$

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

$2 (1) - 3 y = - 6$

Solve the equation for $y$ .

Multiply $2$ by $1$ .

$2 - 3 y = - 6$

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

Subtract $2$ from both sides of the equation.

$- 3 y = - 6 - 2$

Subtract $2$ from $- 6$ .

$- 3 y = - 8$

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.

Dividing two negative values results in a positive value.

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

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

$2 (2) - 3 y = - 6$

Solve the equation for $y$ .

Multiply $2$ by $2$ .

$4 - 3 y = - 6$

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

Subtract $4$ from both sides of the equation.

$- 3 y = - 6 - 4$

Subtract $4$ from $- 6$ .

$- 3 y = - 10$

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.

Dividing two negative values results in a positive value.

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

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

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

Graph Using a Table of Values 2x-3y=-6

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