Pre-Algebra Examples

$4 y - 2 x - 1 = 0$

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

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

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

$4 y - 1 = 2 x$

Step 1.2.2

Add $1$ to both sides of the equation.

$4 y = 2 x + 1$

Step 1.3

Divide each term in $4 y = 2 x + 1$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = 2 x + 1$ by $4$ .

$\frac{4 y}{4} = \frac{2 x}{4} + \frac{1}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{2 x}{4} + \frac{1}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 x}{4} + \frac{1}{4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

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

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Step 1.3.3.1.1

Factor $2$ out of $2 x$ .

$y = \frac{2 (x)}{4} + \frac{1}{4}$

Step 1.3.3.1.2

Cancel the common factors.

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Step 1.3.3.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 x}{2 \cdot 2} + \frac{1}{4}$

Step 1.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 x}{2 \cdot 2} + \frac{1}{4}$

Step 1.3.3.1.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{1}{4}$

Step 1.4

Reorder terms.

$y = \frac{1}{2} x + \frac{1}{4}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{2}$ .

$m = \frac{1}{2}$

Step 3