Precalculus Examples

$y = 4 x - 2$ , $(0, 5)$

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 $4$ .

$m = 4$

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 $4$ and a given point $(0, 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (5) = 4 \cdot (x - (0))$

Step 4

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

$y - 5 = 4 \cdot (x + 0)$

Step 5

Solve for $y$ .

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Step 5.1

Add $x$ and $0$ .

$y - 5 = 4 x$

Step 5.2

Add $5$ to both sides of the equation.

$y = 4 x + 5$

Step 6