Graph Using a Table of Values x+2y=1

$x + 2 y = 1$

Step 1

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

$(- 2) + 2 y = 1$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$- 2 + 2 y = 1$

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

Add $2$ to both sides of the equation.

$2 y = 1 + 2$

Add $1$ and $2$ .

$2 y = 3$

Divide each term in $2 y = 3$ by $2$ and simplify.

Divide each term in $2 y = 3$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Step 3

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

$(- 1) + 2 y = 1$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$- 1 + 2 y = 1$

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

Add $1$ to both sides of the equation.

$2 y = 1 + 1$

Add $1$ and $1$ .

$2 y = 2$

Divide each term in $2 y = 2$ by $2$ and simplify.

Divide each term in $2 y = 2$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$y = 1$

Step 5

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

$(0) + 2 y = 1$

Step 6

Solve the equation for $y$ .

Add $0$ and $2 y$ .

$2 y = 1$

Divide each term in $2 y = 1$ by $2$ and simplify.

Divide each term in $2 y = 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Step 7

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

$(1) + 2 y = 1$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$1 + 2 y = 1$

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

Subtract $1$ from both sides of the equation.

$2 y = 1 - 1$

Subtract $1$ from $1$ .

$2 y = 0$

Divide each term in $2 y = 0$ by $2$ and simplify.

Divide each term in $2 y = 0$ by $2$ .

$\frac{2 y}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{0}{2}$

Divide $y$ by $1$ .

$y = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$y = 0$

Step 9

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

$(2) + 2 y = 1$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$2 + 2 y = 1$

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

Subtract $2$ from both sides of the equation.

$2 y = 1 - 2$

Subtract $2$ from $1$ .

$2 y = - 1$

Divide each term in $2 y = - 1$ by $2$ and simplify.

Divide each term in $2 y = - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 11

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

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

Step 12

Graph Using a Table of Values x+2y=1

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