Graph Using a Table of Values 12x-8y=16

$12 x - 8 y = 16$

Step 1

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

$12 (- 2) - 8 y = 16$

Step 2

Solve the equation for $y$ .

Multiply $12$ by $- 2$ .

$- 24 - 8 y = 16$

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

Add $24$ to both sides of the equation.

$- 8 y = 16 + 24$

Add $16$ and $24$ .

$- 8 y = 40$

Divide each term in $- 8 y = 40$ by $- 8$ and simplify.

Divide each term in $- 8 y = 40$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{40}{- 8}$

Divide $y$ by $1$ .

$y = \frac{40}{- 8}$

Simplify the right side.

Divide $40$ by $- 8$ .

$y = - 5$

Step 3

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

$12 (- 1) - 8 y = 16$

Step 4

Solve the equation for $y$ .

Multiply $12$ by $- 1$ .

$- 12 - 8 y = 16$

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

Add $12$ to both sides of the equation.

$- 8 y = 16 + 12$

Add $16$ and $12$ .

$- 8 y = 28$

Divide each term in $- 8 y = 28$ by $- 8$ and simplify.

Divide each term in $- 8 y = 28$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{28}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{28}{- 8}$

Divide $y$ by $1$ .

$y = \frac{28}{- 8}$

Simplify the right side.

Cancel the common factor of $28$ and $- 8$ .

Factor $4$ out of $28$ .

$y = \frac{4 (7)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$y = \frac{4 \cdot 7}{4 \cdot - 2}$

Cancel the common factor.

$y = \frac{4 \cdot 7}{4 \cdot - 2}$

Rewrite the expression.

$y = \frac{7}{- 2}$

Move the negative in front of the fraction.

$y = - \frac{7}{2}$

Step 5

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

$12 (0) - 8 y = 16$

Step 6

Solve the equation for $y$ .

Simplify $12 (0) - 8 y$ .

Multiply $12$ by $0$ .

$0 - 8 y = 16$

Subtract $8 y$ from $0$ .

$- 8 y = 16$

Divide each term in $- 8 y = 16$ by $- 8$ and simplify.

Divide each term in $- 8 y = 16$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{16}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{16}{- 8}$

Divide $y$ by $1$ .

$y = \frac{16}{- 8}$

Simplify the right side.

Divide $16$ by $- 8$ .

$y = - 2$

Step 7

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

$12 (1) - 8 y = 16$

Step 8

Solve the equation for $y$ .

Multiply $12$ by $1$ .

$12 - 8 y = 16$

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

Subtract $12$ from both sides of the equation.

$- 8 y = 16 - 12$

Subtract $12$ from $16$ .

$- 8 y = 4$

Divide each term in $- 8 y = 4$ by $- 8$ and simplify.

Divide each term in $- 8 y = 4$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{4}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{4}{- 8}$

Divide $y$ by $1$ .

$y = \frac{4}{- 8}$

Simplify the right side.

Cancel the common factor of $4$ and $- 8$ .

Factor $4$ out of $4$ .

$y = \frac{4 (1)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$y = \frac{4 \cdot 1}{4 \cdot - 2}$

Cancel the common factor.

$y = \frac{4 \cdot 1}{4 \cdot - 2}$

Rewrite the expression.

$y = \frac{1}{- 2}$

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 9

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

$12 (2) - 8 y = 16$

Step 10

Solve the equation for $y$ .

Multiply $12$ by $2$ .

$24 - 8 y = 16$

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

Subtract $24$ from both sides of the equation.

$- 8 y = 16 - 24$

Subtract $24$ from $16$ .

$- 8 y = - 8$

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

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

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 8$ by $- 8$ .

$y = 1$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 5 \\ - 1 & - \frac{7}{2} \\ 0 & - 2 \\ 1 & - \frac{1}{2} \\ 2 & 1 \end{array}$

Step 12

Graph Using a Table of Values 12x-8y=16

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