Precalculus Examples

y = 3 x - 21

$y = 3 x - 21$ ,

(- 7, 0)

$(- 7, 0)$

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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is

3

$3$ .

m = 3

$m = 3$

m = 3

$m = 3$

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

3

$3$ and a given point

(- 7, 0)

$(- 7, 0)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

y - (0) = 3 \cdot (x - (- 7))

$y - (0) = 3 \cdot (x - (- 7))$

Step 4

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

y + 0 = 3 \cdot (x + 7)

$y + 0 = 3 \cdot (x + 7)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Add

y

$y$ and

0

$0$ .

y = 3 \cdot (x + 7)

$y = 3 \cdot (x + 7)$

Step 5.2

Simplify

3 \cdot (x + 7)

$3 \cdot (x + 7)$ .

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Step 5.2.1

Apply the distributive property.

y = 3 x + 3 \cdot 7

$y = 3 x + 3 \cdot 7$

Step 5.2.2

Multiply

3

$3$ by

7

$7$ .

y = 3 x + 21

$y = 3 x + 21$

y = 3 x + 21

$y = 3 x + 21$

y = 3 x + 21

$y = 3 x + 21$

Step 6

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