Algebra Examples

$- 2 x - y = 1$ $- 6 x = 3 y + 3$

Step 1

Graph $- 2 x - y = 1$ .

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Add $2 x$ to both sides of the equation.

$- y = 1 + 2 x$

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.1.2.2.2

Divide $y$ by $1$ .

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

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 $1$ by $- 1$ .

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

Step 1.1.2.3.1.2

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y = - 1 - 1 \cdot (2 x)$

Step 1.1.2.3.1.3

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y = - 1 - (2 x)$

Step 1.1.2.3.1.4

Multiply $2$ by $- 1$ .

$y = - 1 - 2 x$

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 $- 1$ and $- 2 x$ .

$y = - 2 x - 1$

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 $y = m x + b$ .

$m = - 2$

$b = - 1$

Step 1.3.2

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

Slope: $- 2$

y-intercept: $(0, - 1)$

Slope: $- 2$

y-intercept: $(0, - 1)$

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

Reorder $- 1$ and $- 2 x$ .

$y = - 2 x - 1$

Step 1.4.2

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

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

Step 1.5

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

Slope: $- 2$

y-intercept: $(0, - 1)$

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

Slope: $- 2$

y-intercept: $(0, - 1)$

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

Step 2

Plot each graph on the same coordinate system.

$- 2 x - y = 1$

$- 6 x = 3 y + 3$

Step 3