Precalculus Examples

$y = 5 x$ , $(2, 2)$

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 $5$ .

$m = 5$

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

$y - (2) = 5 \cdot (x - (2))$

Step 4

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

$y - 2 = 5 \cdot (x - 2)$

Step 5

Solve for $y$ .

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Step 5.1

Simplify $5 \cdot (x - 2)$ .

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Step 5.1.1

Rewrite.

$y - 2 = 0 + 0 + 5 \cdot (x - 2)$

Step 5.1.2

Simplify by adding zeros.

$y - 2 = 5 \cdot (x - 2)$

Step 5.1.3

Apply the distributive property.

$y - 2 = 5 x + 5 \cdot - 2$

Step 5.1.4

Multiply $5$ by $- 2$ .

$y - 2 = 5 x - 10$

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 $2$ to both sides of the equation.

$y = 5 x - 10 + 2$

Step 5.2.2

Add $- 10$ and $2$ .

$y = 5 x - 8$

Step 6