Precalculus Examples

$y = x + 4$

Choose a point that the parallel line will pass through.

$(0, 0)$

Use the slope-intercept form to find the slope.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = 1$

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

Use the slope $1$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 1 \cdot (x - (0))$

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

$y + 0 = 1 \cdot (x + 0)$

Solve for $y$ .

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Add $y$ and $0$ .

$y = 1 \cdot (x + 0)$

Simplify $1 \cdot (x + 0)$ .

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Multiply $x + 0$ by $1$ .

$y = x + 0$

Add $x$ and $0$ .

$y = x$

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