Algebra Examples

$y - 3 = \frac{1}{2} (x - 4)$

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

Simplify the right side.

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Step 2.1.1

Simplify $\frac{1}{2} (x - 4)$ .

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Step 2.1.1.1

Apply the distributive property.

$y - 3 = \frac{1}{2} x + \frac{1}{2} \cdot - 4$

Step 2.1.1.2

Combine $\frac{1}{2}$ and $x$ .

$y - 3 = \frac{x}{2} + \frac{1}{2} \cdot - 4$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $- 4$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.2

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

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Step 2.2.1

Add $3$ to both sides of the equation.

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

Step 2.2.2

Add $- 2$ and $3$ .

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

Step 2.3

Reorder terms.

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