Pre-Algebra Examples

$4 x - 6 y = 6$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $4 x$ from both sides of the equation.

$- 6 y = 6 - 4 x$

Step 1.2

Divide each term in $- 6 y = 6 - 4 x$ by $- 6$ and simplify.

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Step 1.2.1

Divide each term in $- 6 y = 6 - 4 x$ by $- 6$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 6$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

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 $6$ by $- 6$ .

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

Step 1.2.3.1.2

Cancel the common factor of $- 4$ and $- 6$ .

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Step 1.2.3.1.2.1

Factor $- 2$ out of $- 4 x$ .

$y = - 1 + \frac{- 2 (2 x)}{- 6}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $- 2$ out of $- 6$ .

$y = - 1 + \frac{- 2 (2 x)}{- 2 (3)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = - 1 + \frac{- 2 (2 x)}{- 2 \cdot 3}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = - 1 + \frac{2 x}{3}$

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 $- 1$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} - 1$

Step 2.3

Reorder terms.

$y = \frac{2}{3} x - 1$

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 $y = m x + b$ .

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

$b = - 1$

Step 3.2

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

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

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

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

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

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

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

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Step 4.1.1

Reorder $- 1$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} - 1$

Step 4.1.2

Reorder terms.

$y = \frac{2}{3} x - 1$

Step 4.2

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

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

Step 5

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

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

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

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

Step 6