Graph Using a Table of Values 9x-6y=18

$9 x - 6 y = 18$

Step 1

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

$9 (- 2) - 6 y = 18$

Step 2

Solve the equation for $y$ .

Multiply $9$ by $- 2$ .

$- 18 - 6 y = 18$

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

Add $18$ to both sides of the equation.

$- 6 y = 18 + 18$

Add $18$ and $18$ .

$- 6 y = 36$

Divide each term in $- 6 y = 36$ by $- 6$ and simplify.

Divide each term in $- 6 y = 36$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{36}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{36}{- 6}$

Divide $y$ by $1$ .

$y = \frac{36}{- 6}$

Simplify the right side.

Divide $36$ by $- 6$ .

$y = - 6$

Step 3

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

$9 (- 1) - 6 y = 18$

Step 4

Solve the equation for $y$ .

Multiply $9$ by $- 1$ .

$- 9 - 6 y = 18$

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

Add $9$ to both sides of the equation.

$- 6 y = 18 + 9$

Add $18$ and $9$ .

$- 6 y = 27$

Divide each term in $- 6 y = 27$ by $- 6$ and simplify.

Divide each term in $- 6 y = 27$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{27}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{27}{- 6}$

Divide $y$ by $1$ .

$y = \frac{27}{- 6}$

Simplify the right side.

Cancel the common factor of $27$ and $- 6$ .

Factor $3$ out of $27$ .

$y = \frac{3 (9)}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$y = \frac{3 \cdot 9}{3 \cdot - 2}$

Cancel the common factor.

$y = \frac{3 \cdot 9}{3 \cdot - 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

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

$9 (0) - 6 y = 18$

Step 6

Solve the equation for $y$ .

Simplify $9 (0) - 6 y$ .

Multiply $9$ by $0$ .

$0 - 6 y = 18$

Subtract $6 y$ from $0$ .

$- 6 y = 18$

Divide each term in $- 6 y = 18$ by $- 6$ and simplify.

Divide each term in $- 6 y = 18$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{18}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{18}{- 6}$

Divide $y$ by $1$ .

$y = \frac{18}{- 6}$

Simplify the right side.

Divide $18$ by $- 6$ .

$y = - 3$

Step 7

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

$9 (1) - 6 y = 18$

Step 8

Solve the equation for $y$ .

Multiply $9$ by $1$ .

$9 - 6 y = 18$

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

Subtract $9$ from both sides of the equation.

$- 6 y = 18 - 9$

Subtract $9$ from $18$ .

$- 6 y = 9$

Divide each term in $- 6 y = 9$ by $- 6$ and simplify.

Divide each term in $- 6 y = 9$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{9}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{9}{- 6}$

Divide $y$ by $1$ .

$y = \frac{9}{- 6}$

Simplify the right side.

Cancel the common factor of $9$ and $- 6$ .

Factor $3$ out of $9$ .

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

Cancel the common factors.

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 9

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

$9 (2) - 6 y = 18$

Step 10

Solve the equation for $y$ .

Multiply $9$ by $2$ .

$18 - 6 y = 18$

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

Subtract $18$ from both sides of the equation.

$- 6 y = 18 - 18$

Subtract $18$ from $18$ .

$- 6 y = 0$

Divide each term in $- 6 y = 0$ by $- 6$ and simplify.

Divide each term in $- 6 y = 0$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Divide $y$ by $1$ .

$y = \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$y = 0$

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 9x-6y=18

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