Algebra Examples

$y - 3 = \frac{1}{2} (x - 6)$

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

Simplify the right side.

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Step 1.2.1

Simplify $\frac{1}{2} (x - 6)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 3 = \frac{1}{2} x + \frac{1}{2} \cdot - 6$

Step 1.2.1.2

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

$y - 3 = \frac{x}{2} + \frac{1}{2} \cdot - 6$

Step 1.2.1.3

Cancel the common factor of $2$ .

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Step 1.2.1.3.1

Factor $2$ out of $- 6$ .

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

Step 1.2.1.3.2

Cancel the common factor.

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

Step 1.2.1.3.3

Rewrite the expression.

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

Step 1.3

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

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Step 1.3.1

Add $3$ to both sides of the equation.

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

Step 1.3.2

Combine the opposite terms in $\frac{x}{2} - 3 + 3$ .

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Step 1.3.2.1

Add $- 3$ and $3$ .

$y = \frac{x}{2} + 0$

Step 1.3.2.2

Add $\frac{x}{2}$ and $0$ .

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

Step 1.4

Reorder terms.

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

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

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

$b = 0$

Step 2.2

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 0)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 0)$

Step 3