Algebra Examples

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

Step 1

Write in slope-intercept form $y = m x + b$ to identify the slope $m$ .

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Step 1.1

Write in $y = m x + b$ form.

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Step 1.1.1

Solve for $y$ .

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Step 1.1.1.1

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

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Step 1.1.1.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{2} (x + 2)$

Step 1.1.1.1.2

Simplify by adding zeros.

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

Step 1.1.1.1.3

Apply the distributive property.

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

Step 1.1.1.1.4

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

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

Step 1.1.1.1.5

Cancel the common factor of $2$ .

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Step 1.1.1.1.5.1

Cancel the common factor.

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

Step 1.1.1.1.5.2

Rewrite the expression.

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

Step 1.1.1.2

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

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Step 1.1.1.2.1

Add $3$ to both sides of the equation.

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

Step 1.1.1.2.2

Add $1$ and $3$ .

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

Step 1.1.2

Reorder terms.

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

Step 1.2

Using slope-intercept form $y = m x + b$ , identify the slope $m$ .

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

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

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

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

Step 2

Pick any $x$ -value, then substitute into the equation and simplify to find a point on the line.

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Step 2.1

Substitute $1$ for $x$ .

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

Step 2.2

Multiply $\frac{1}{2}$ by $1$ .

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

Step 2.3

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.4

Combine $4$ and $\frac{2}{2}$ .

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $4$ by $2$ .

$y = \frac{1 + 8}{2}$

Step 2.6.2

Add $1$ and $8$ .

$y = \frac{9}{2}$

Step 2.7

Since $y = \frac{9}{2}$ when $x = 1$ , $(1, \frac{9}{2})$ is a point on the line.

$(1, \frac{9}{2})$

Step 3

Plug in the values of the found point and the value of the slope into the point-slope form $y - y_{1} = m (x - x_{1})$ .

$y - \frac{9}{2} = \frac{1}{2} (x - 1)$

Step 4