Examples

y = x - 2

$y = x - 2$

Step 1

Choose a point that the parallel line will pass through.

(0, 0)

$(0, 0)$

Step 2

Use the slope-intercept form to find the slope.

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Step 2.1

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 2.2

Using the slope-intercept form, the slope is

1

$1$ .

m = 1

$m = 1$

m = 1

$m = 1$

Step 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 4

Use the slope

1

$1$ and a given point

(0, 0)

$(0, 0)$ 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) = 1 \cdot (x - (0))

$y - (0) = 1 \cdot (x - (0))$

Step 5

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

y + 0 = 1 \cdot (x + 0)

$y + 0 = 1 \cdot (x + 0)$

Step 6

Solve for

y

$y$ .

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Step 6.1

Add

y

$y$ and

0

$0$ .

y = 1 \cdot (x + 0)

$y = 1 \cdot (x + 0)$

Step 6.2

Simplify

1 \cdot (x + 0)

$1 \cdot (x + 0)$ .

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Step 6.2.1

Multiply

x + 0

$x + 0$ by

1

$1$ .

y = x + 0

$y = x + 0$

Step 6.2.2

Add

x

$x$ and

0

$0$ .

y = x

$y = x$

y = x

$y = x$

y = x

$y = x$

Step 7

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