Precalculus Examples

y = 9 x - 6

$y = 9 x - 6$ ,

(1, 13)

$(1, 13)$

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

9

$9$ .

m = 9

$m = 9$

m = 9

$m = 9$

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

9

$9$ and a given point

(1, 13)

$(1, 13)$ 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 - (13) = 9 \cdot (x - (1))

$y - (13) = 9 \cdot (x - (1))$

Step 4

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

y - 13 = 9 \cdot (x - 1)

$y - 13 = 9 \cdot (x - 1)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Simplify

9 \cdot (x - 1)

$9 \cdot (x - 1)$ .

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Step 5.1.1

Rewrite.

y - 13 = 0 + 0 + 9 \cdot (x - 1)

$y - 13 = 0 + 0 + 9 \cdot (x - 1)$

Step 5.1.2

Simplify by adding zeros.

y - 13 = 9 \cdot (x - 1)

$y - 13 = 9 \cdot (x - 1)$

Step 5.1.3

Apply the distributive property.

y - 13 = 9 x + 9 \cdot - 1

$y - 13 = 9 x + 9 \cdot - 1$

Step 5.1.4

Multiply

9

$9$ by

- 1

$- 1$ .

y - 13 = 9 x - 9

$y - 13 = 9 x - 9$

y - 13 = 9 x - 9

$y - 13 = 9 x - 9$

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

13

$13$ to both sides of the equation.

y = 9 x - 9 + 13

$y = 9 x - 9 + 13$

Step 5.2.2

Add

- 9

$- 9$ and

13

$13$ .

y = 9 x + 4

$y = 9 x + 4$

y = 9 x + 4

$y = 9 x + 4$

y = 9 x + 4

$y = 9 x + 4$

Step 6

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