Graph Using a Table of Values -5x-3y=22

$- 5 x - 3 y = 22$

Step 1

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

$- 5 \cdot - 2 - 3 y = 22$

Step 2

Solve the equation for $y$ .

Multiply $- 5$ by $- 2$ .

$10 - 3 y = 22$

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

Subtract $10$ from both sides of the equation.

$- 3 y = 22 - 10$

Subtract $10$ from $22$ .

$- 3 y = 12$

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 3

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

$- 5 \cdot - 1 - 3 y = 22$

Step 4

Solve the equation for $y$ .

Multiply $- 5$ by $- 1$ .

$5 - 3 y = 22$

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

Subtract $5$ from both sides of the equation.

$- 3 y = 22 - 5$

Subtract $5$ from $22$ .

$- 3 y = 17$

Divide each term in $- 3 y = 17$ by $- 3$ and simplify.

Divide each term in $- 3 y = 17$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{17}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{17}{- 3}$

Divide $y$ by $1$ .

$y = \frac{17}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{17}{3}$

Step 5

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

$- 5 \cdot 0 - 3 y = 22$

Step 6

Solve the equation for $y$ .

Simplify $- 5 \cdot 0 - 3 y$ .

Multiply $- 5$ by $0$ .

$0 - 3 y = 22$

Subtract $3 y$ from $0$ .

$- 3 y = 22$

Divide each term in $- 3 y = 22$ by $- 3$ and simplify.

Divide each term in $- 3 y = 22$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{22}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{22}{- 3}$

Divide $y$ by $1$ .

$y = \frac{22}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{22}{3}$

Step 7

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

$- 5 \cdot 1 - 3 y = 22$

Step 8

Solve the equation for $y$ .

Multiply $- 5$ by $1$ .

$- 5 - 3 y = 22$

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

Add $5$ to both sides of the equation.

$- 3 y = 22 + 5$

Add $22$ and $5$ .

$- 3 y = 27$

Divide each term in $- 3 y = 27$ by $- 3$ and simplify.

Divide each term in $- 3 y = 27$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{27}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{27}{- 3}$

Divide $y$ by $1$ .

$y = \frac{27}{- 3}$

Simplify the right side.

Divide $27$ by $- 3$ .

$y = - 9$

Step 9

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

$- 5 \cdot 2 - 3 y = 22$

Step 10

Solve the equation for $y$ .

Multiply $- 5$ by $2$ .

$- 10 - 3 y = 22$

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

Add $10$ to both sides of the equation.

$- 3 y = 22 + 10$

Add $22$ and $10$ .

$- 3 y = 32$

Divide each term in $- 3 y = 32$ by $- 3$ and simplify.

Divide each term in $- 3 y = 32$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{32}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{32}{- 3}$

Divide $y$ by $1$ .

$y = \frac{32}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{32}{3}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 4 \\ - 1 & - \frac{17}{3} \\ 0 & - \frac{22}{3} \\ 1 & - 9 \\ 2 & - \frac{32}{3} \end{array}$

Step 12

Graph Using a Table of Values -5x-3y=22

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