Examples

y = x + \frac{1}{2}

$y = x + \frac{1}{2}$ ,

(- 4, 1)

$(- 4, 1)$

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

1

$1$ .

m = 1

$m = 1$

m = 1

$m = 1$

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

1

$1$ and a given point

(- 4, 1)

$(- 4, 1)$ 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 - (1) = 1 \cdot (x - (- 4))

$y - (1) = 1 \cdot (x - (- 4))$

Step 4

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

y - 1 = 1 \cdot (x + 4)

$y - 1 = 1 \cdot (x + 4)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Multiply

x + 4

$x + 4$ by

1

$1$ .

y - 1 = x + 4

$y - 1 = x + 4$

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

1

$1$ to both sides of the equation.

y = x + 4 + 1

$y = x + 4 + 1$

Step 5.2.2

Add

4

$4$ and

1

$1$ .

y = x + 5

$y = x + 5$

y = x + 5

$y = x + 5$

y = x + 5

$y = x + 5$

Step 6

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