Algebra 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

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

m_{perpendicular} = - \frac{1}{1}

$m_{perpendicular} = - \frac{1}{1}$

Step 3

Simplify

- \frac{1}{1}

$- \frac{1}{1}$ to find the slope of the perpendicular line.

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Step 3.1

Cancel the common factor of

1

$1$ .

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Step 3.1.1

Cancel the common factor.

m_{perpendicular} = - \frac{1}{1}

$m_{perpendicular} = - \frac{1}{1}$

Step 3.1.2

Rewrite the expression.

m_{perpendicular} = - 1 \cdot 1

$m_{perpendicular} = - 1 \cdot 1$

m_{perpendicular} = - 1 \cdot 1

$m_{perpendicular} = - 1 \cdot 1$

Step 3.2

Multiply

- 1

$- 1$ by

1

$1$ .

m_{perpendicular} = - 1

$m_{perpendicular} = - 1$

m_{perpendicular} = - 1

$m_{perpendicular} = - 1$

Step 4

Find the equation of the perpendicular line using the point-slope formula.

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Step 4.1

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 4.2

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

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

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

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

Simplify

- 1 \cdot (x - 2)

$- 1 \cdot (x - 2)$ .

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Step 5.1.1

Rewrite.

y - 6 = 0 + 0 - 1 \cdot (x - 2)

$y - 6 = 0 + 0 - 1 \cdot (x - 2)$

Step 5.1.2

Simplify by adding zeros.

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

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

Step 5.1.3

Apply the distributive property.

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

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

Step 5.1.4

Simplify the expression.

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Step 5.1.4.1

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

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

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

Step 5.1.4.2

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

y - 6 = - x + 2

$y - 6 = - x + 2$

y - 6 = - x + 2

$y - 6 = - x + 2$

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 + 8

$y = - x + 8$

y = - x + 8

$y = - x + 8$

y = - x + 8

$y = - x + 8$

Step 6

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