Precalculus Examples

$4 y = 2 x + 10$

Step 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

Rewrite in slope-intercept form.

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Step 2.1

Divide each term in $4 y = 2 x + 10$ by $4$ and simplify.

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Step 2.1.1

Divide each term in $4 y = 2 x + 10$ by $4$ .

$\frac{4 y}{4} = \frac{2 x}{4} + \frac{10}{4}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $4$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{2 x}{4} + \frac{10}{4}$

Step 2.1.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 x}{4} + \frac{10}{4}$

$y = \frac{2 x}{4} + \frac{10}{4}$

$y = \frac{2 x}{4} + \frac{10}{4}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

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

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Step 2.1.3.1.1.1

Factor $2$ out of $2 x$ .

$y = \frac{2 (x)}{4} + \frac{10}{4}$

Step 2.1.3.1.1.2

Cancel the common factors.

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Step 2.1.3.1.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 x}{2 \cdot 2} + \frac{10}{4}$

Step 2.1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 x}{2 \cdot 2} + \frac{10}{4}$

Step 2.1.3.1.1.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{10}{4}$

$y = \frac{x}{2} + \frac{10}{4}$

$y = \frac{x}{2} + \frac{10}{4}$

Step 2.1.3.1.2

Cancel the common factor of $10$ and $4$ .

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Step 2.1.3.1.2.1

Factor $2$ out of $10$ .

$y = \frac{x}{2} + \frac{2 (5)}{4}$

Step 2.1.3.1.2.2

Cancel the common factors.

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Step 2.1.3.1.2.2.1

Factor $2$ out of $4$ .

$y = \frac{x}{2} + \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.1.3.1.2.2.2

Cancel the common factor.

$y = \frac{x}{2} + \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.1.3.1.2.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{5}{2}$

$y = \frac{x}{2} + \frac{5}{2}$

$y = \frac{x}{2} + \frac{5}{2}$

$y = \frac{x}{2} + \frac{5}{2}$

$y = \frac{x}{2} + \frac{5}{2}$

$y = \frac{x}{2} + \frac{5}{2}$

Step 2.2

Reorder terms.

$y = \frac{1}{2} x + \frac{5}{2}$

$y = \frac{1}{2} x + \frac{5}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$