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

$2 x + 3 y = 6$

Step 1

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

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

Step 2

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 $4$ .

$3 y = 10$

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 $1$ .

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

Step 3

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

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

Step 4

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 $2$ .

$3 y = 8$

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 $1$ .

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

Step 5

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

$2 (0) + 3 y = 6$

Step 6

Solve the equation for $y$ .

Simplify $2 (0) + 3 y$ .

Multiply $2$ by $0$ .

$0 + 3 y = 6$

Add $0$ and $3 y$ .

$3 y = 6$

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 $3$ .

$y = 2$

Step 7

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

$2 (1) + 3 y = 6$

Step 8

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 $6$ .

$3 y = 4$

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 $1$ .

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

Step 9

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

$2 (2) + 3 y = 6$

Step 10

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 $6$ .

$3 y = 2$

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 $1$ .

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

Step 11

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

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

Step 12

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

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