Precalculus Examples

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

Step 1

Use the slope-intercept form to find the slope.

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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

Using the slope-intercept form, the slope is $1$ .

$m = 1$

Step 2

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 3

Use the slope $1$ and a given point $(- 4, 1)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (1) = 1 \cdot (x - (- 4))$

Step 4

Simplify the equation and keep it in point-slope form.

$y - 1 = 1 \cdot (x + 4)$

Step 5

Solve for $y$ .

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Step 5.1

Multiply $x + 4$ by $1$ .

$y - 1 = x + 4$

Step 5.2

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

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Step 5.2.1

Add $1$ to both sides of the equation.

$y = x + 4 + 1$

Step 5.2.2

Add $4$ and $1$ .

$y = x + 5$

Step 6

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