Algebra Examples

$x = - 2$ $3 x - 2 y = - 18$

Step 1

Graph $x = - 2$ .

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Step 1.1

Since $x = - 2$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 1.2

Find two points on the line.

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

Step 1.3

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

Slope: Undefined

y-intercept: No y-intercept

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

Slope: Undefined

y-intercept: No y-intercept

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

Step 2

Graph $3 x - 2 y = - 18$ .

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Step 2.1

Solve for $y$ .

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Step 2.1.1

Subtract $3 x$ from both sides of the equation.

$- 2 y = - 18 - 3 x$

Step 2.1.2

Divide each term in $- 2 y = - 18 - 3 x$ by $- 2$ and simplify.

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Step 2.1.2.1

Divide each term in $- 2 y = - 18 - 3 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 18}{- 2} + \frac{- 3 x}{- 2}$

Step 2.1.2.2

Simplify the left side.

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Step 2.1.2.2.1

Cancel the common factor of $- 2$ .

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Step 2.1.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 18}{- 2} + \frac{- 3 x}{- 2}$

Step 2.1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 18}{- 2} + \frac{- 3 x}{- 2}$

Step 2.1.2.3

Simplify the right side.

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Step 2.1.2.3.1

Simplify each term.

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Step 2.1.2.3.1.1

Divide $- 18$ by $- 2$ .

$y = 9 + \frac{- 3 x}{- 2}$

Step 2.1.2.3.1.2

Dividing two negative values results in a positive value.

$y = 9 + \frac{3 x}{2}$

Step 2.2

Rewrite in slope-intercept form.

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Step 2.2.1

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 2.2.2

Reorder $9$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} + 9$

Step 2.2.3

Reorder terms.

$y = \frac{3}{2} x + 9$

Step 2.3

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

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Step 2.3.1

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

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

$b = 9$

Step 2.3.2

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

Slope: $\frac{3}{2}$

y-intercept: $(0, 9)$

Slope: $\frac{3}{2}$

y-intercept: $(0, 9)$

Step 2.4

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 2.4.1

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

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Step 2.4.1.1

Reorder $9$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} + 9$

Step 2.4.1.2

Reorder terms.

$y = \frac{3}{2} x + 9$

Step 2.4.2

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

$\begin{array}{c} x & y \\ 0 & 9 \\ 2 & 12 \end{array}$

Step 2.5

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

Slope: $\frac{3}{2}$

y-intercept: $(0, 9)$

$\begin{array}{c} x & y \\ 0 & 9 \\ 2 & 12 \end{array}$

Slope: $\frac{3}{2}$

y-intercept: $(0, 9)$

$\begin{array}{c} x & y \\ 0 & 9 \\ 2 & 12 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$x = - 2$

$3 x - 2 y = - 18$

Step 4