Pre-Algebra Examples

$12 x - 3 y = 18$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $12 x$ from both sides of the equation.

$- 3 y = 18 - 12 x$

Step 1.2

Divide each term in $- 3 y = 18 - 12 x$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y = 18 - 12 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{18}{- 3} + \frac{- 12 x}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{18}{- 3} + \frac{- 12 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{- 3} + \frac{- 12 x}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $18$ by $- 3$ .

$y = - 6 + \frac{- 12 x}{- 3}$

Step 1.2.3.1.2

Cancel the common factor of $- 12$ and $- 3$ .

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Step 1.2.3.1.2.1

Factor $- 3$ out of $- 12 x$ .

$y = - 6 + \frac{- 3 (4 x)}{- 3}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $- 3$ out of $- 3$ .

$y = - 6 + \frac{- 3 (4 x)}{- 3 (1)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = - 6 + \frac{- 3 (4 x)}{- 3 \cdot 1}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = - 6 + \frac{4 x}{1}$

Step 1.2.3.1.2.2.4

Divide $4 x$ by $1$ .

$y = - 6 + 4 x$

Step 2

Rewrite in slope-intercept form.

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Step 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

Reorder $- 6$ and $4 x$ .

$y = 4 x - 6$

Step 3

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

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Step 3.1

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

$m = 4$

$b = - 6$

Step 3.2

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

Slope: $4$

y-intercept: $(0, - 6)$

Slope: $4$

y-intercept: $(0, - 6)$

Step 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 4.1

Reorder $- 6$ and $4 x$ .

$y = 4 x - 6$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & - 6 \\ 1 & - 2 \end{array}$

Step 5

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

Slope: $4$

y-intercept: $(0, - 6)$

$\begin{array}{c} x & y \\ 0 & - 6 \\ 1 & - 2 \end{array}$

Step 6