Pre-Algebra Examples

$x - 2 y = - 4$ , $- x + 2 y = 4$

Step 1

Graph $x - 2 y = - 4$ .

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Subtract $x$ from both sides of the equation.

$- 2 y = - 4 - x$

Step 1.1.2

Divide each term in $- 2 y = - 4 - x$ by $- 2$ and simplify.

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Step 1.1.2.1

Divide each term in $- 2 y = - 4 - x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 4}{- 2} + \frac{- x}{- 2}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 4}{- 2} + \frac{- x}{- 2}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4}{- 2} + \frac{- x}{- 2}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $- 4$ by $- 2$ .

$y = 2 + \frac{- x}{- 2}$

Step 1.1.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.2

Rewrite in slope-intercept form.

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Step 1.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2.2

Reorder $2$ and $\frac{x}{2}$ .

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

Step 1.2.3

Reorder terms.

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

Step 1.3

Use the slope-intercept form to find the slope and y-intercept.

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Step 1.3.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

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

$b = 2$

Step 1.3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

Step 1.4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 1.4.1

Write in $y = m x + b$ form.

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Step 1.4.1.1

Reorder $2$ and $\frac{x}{2}$ .

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

Step 1.4.1.2

Reorder terms.

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

Step 1.4.2

Create a table of the $x$ and $y$ values.

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

Step 1.5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

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

Step 2

Plot each graph on the same coordinate system.

$x - 2 y = - 4$

$- x + 2 y = 4$

Step 3