Graph Using a Table of Values 4x+3y=12

$4 x + 3 y = 12$

Step 1

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

$4 (- 2) + 3 y = 12$

Step 2

Solve the equation for $y$ .

Multiply $4$ by $- 2$ .

$- 8 + 3 y = 12$

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

Add $8$ to both sides of the equation.

$3 y = 12 + 8$

Add $12$ and $8$ .

$3 y = 20$

Divide each term in $3 y = 20$ by $3$ and simplify.

Divide each term in $3 y = 20$ by $3$ .

$\frac{3 y}{3} = \frac{20}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{20}{3}$

Divide $y$ by $1$ .

$y = \frac{20}{3}$

Step 3

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

$4 (- 1) + 3 y = 12$

Step 4

Solve the equation for $y$ .

Multiply $4$ by $- 1$ .

$- 4 + 3 y = 12$

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 $1$ .

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

Step 5

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

$4 (0) + 3 y = 12$

Step 6

Solve the equation for $y$ .

Simplify $4 (0) + 3 y$ .

Multiply $4$ by $0$ .

$0 + 3 y = 12$

Add $0$ and $3 y$ .

$3 y = 12$

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 $y$ .

$4 (1) + 3 y = 12$

Step 8

Solve the equation for $y$ .

Multiply $4$ by $1$ .

$4 + 3 y = 12$

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 $1$ .

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

Step 9

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

$4 (2) + 3 y = 12$

Step 10

Solve the equation for $y$ .

Multiply $4$ by $2$ .

$8 + 3 y = 12$

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

Subtract $8$ from both sides of the equation.

$3 y = 12 - 8$

Subtract $8$ from $12$ .

$3 y = 4$

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 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{20}{3} \\ - 1 & \frac{16}{3} \\ 0 & 4 \\ 1 & \frac{8}{3} \\ 2 & \frac{4}{3} \end{array}$

Step 12

Graph Using a Table of Values 4x+3y=12

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