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

$3 x + 2 y = 6$

Step 1

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

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

Step 2

Solve the equation for $y$ .

Multiply $3$ by $- 2$ .

$- 6 + 2 y = 6$

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

Add $6$ to both sides of the equation.

$2 y = 6 + 6$

Add $6$ and $6$ .

$2 y = 12$

Divide each term in $2 y = 12$ by $2$ and simplify.

Divide each term in $2 y = 12$ by $2$ .

$\frac{2 y}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{12}{2}$

Divide $y$ by $1$ .

$y = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$y = 6$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Multiply $3$ by $- 1$ .

$- 3 + 2 y = 6$

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

Add $3$ to both sides of the equation.

$2 y = 6 + 3$

Add $6$ and $3$ .

$2 y = 9$

Divide each term in $2 y = 9$ by $2$ and simplify.

Divide each term in $2 y = 9$ by $2$ .

$\frac{2 y}{2} = \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{9}{2}$

Divide $y$ by $1$ .

$y = \frac{9}{2}$

Step 5

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

$3 (0) + 2 y = 6$

Step 6

Solve the equation for $y$ .

Simplify $3 (0) + 2 y$ .

Multiply $3$ by $0$ .

$0 + 2 y = 6$

Add $0$ and $2 y$ .

$2 y = 6$

Divide each term in $2 y = 6$ by $2$ and simplify.

Divide each term in $2 y = 6$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$y = 3$

Step 7

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

$3 (1) + 2 y = 6$

Step 8

Solve the equation for $y$ .

Multiply $3$ by $1$ .

$3 + 2 y = 6$

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

Subtract $3$ from both sides of the equation.

$2 y = 6 - 3$

Subtract $3$ from $6$ .

$2 y = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Step 9

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

$3 (2) + 2 y = 6$

Step 10

Solve the equation for $y$ .

Multiply $3$ by $2$ .

$6 + 2 y = 6$

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

Subtract $6$ from both sides of the equation.

$2 y = 6 - 6$

Subtract $6$ from $6$ .

$2 y = 0$

Divide each term in $2 y = 0$ by $2$ and simplify.

Divide each term in $2 y = 0$ by $2$ .

$\frac{2 y}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{0}{2}$

Divide $y$ by $1$ .

$y = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$y = 0$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 6 \\ - 1 & \frac{9}{2} \\ 0 & 3 \\ 1 & \frac{3}{2} \\ 2 & 0 \end{array}$

Step 12

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

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