Precalculus Examples

y = x - 2

$y = x - 2$ ,

(2, 6)

$(2, 6)$

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

(2, 6)

$(2, 6)$ 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 - (6) = 1 \cdot (x - (2))

$y - (6) = 1 \cdot (x - (2))$

Step 4

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

y - 6 = 1 \cdot (x - 2)

$y - 6 = 1 \cdot (x - 2)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Multiply

x - 2

$x - 2$ by

1

$1$ .

y - 6 = x - 2

$y - 6 = x - 2$

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

6

$6$ to both sides of the equation.

y = x - 2 + 6

$y = x - 2 + 6$

Step 5.2.2

Add

- 2

$- 2$ and

6

$6$ .

y = x + 4

$y = x + 4$

y = x + 4

$y = x + 4$

y = x + 4

$y = x + 4$

Step 6

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