Pre-Algebra Examples

$4 x + 2 y = 6$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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

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

$2 y = 6 - 4 x$

Step 1.3

Divide each term in $2 y = 6 - 4 x$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 y = 6 - 4 x$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 4 x}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 4 x}{2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{2} + \frac{- 4 x}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $6$ by $2$ .

$y = 3 + \frac{- 4 x}{2}$

Step 1.3.3.1.2

Cancel the common factor of $- 4$ and $2$ .

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Step 1.3.3.1.2.1

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

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

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $2$ out of $2$ .

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

Step 1.3.3.1.2.2.2

Cancel the common factor.

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

Step 1.3.3.1.2.2.3

Rewrite the expression.

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

Step 1.3.3.1.2.2.4

Divide $- 2 x$ by $1$ .

$y = 3 - 2 x$

Step 1.4

Reorder $3$ and $- 2 x$ .

$y = - 2 x + 3$

Step 2

Using the slope-intercept form, the slope is $- 2$ .

$m = - 2$

Step 3