Precalculus Examples

y = 3 x - 21

$y = 3 x - 21$ ,

(7, 9)

$(7, 9)$

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, 9)

$(7, 9)$ 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 - (9) = 3 \cdot (x - (7))

$y - (9) = 3 \cdot (x - (7))$

Step 4

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

y - 9 = 3 \cdot (x - 7)

$y - 9 = 3 \cdot (x - 7)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Simplify

3 \cdot (x - 7)

$3 \cdot (x - 7)$ .

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Step 5.1.1

Rewrite.

y - 9 = 0 + 0 + 3 \cdot (x - 7)

$y - 9 = 0 + 0 + 3 \cdot (x - 7)$

Step 5.1.2

Simplify by adding zeros.

y - 9 = 3 \cdot (x - 7)

$y - 9 = 3 \cdot (x - 7)$

Step 5.1.3

Apply the distributive property.

y - 9 = 3 x + 3 \cdot - 7

$y - 9 = 3 x + 3 \cdot - 7$

Step 5.1.4

Multiply

3

$3$ by

- 7

$- 7$ .

y - 9 = 3 x - 21

$y - 9 = 3 x - 21$

y - 9 = 3 x - 21

$y - 9 = 3 x - 21$

Step 5.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 5.2.1

Add

9

$9$ to both sides of the equation.

y = 3 x - 21 + 9

$y = 3 x - 21 + 9$

Step 5.2.2

Add

- 21

$- 21$ and

9

$9$ .

y = 3 x - 12

$y = 3 x - 12$

y = 3 x - 12

$y = 3 x - 12$

y = 3 x - 12

$y = 3 x - 12$

Step 6

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