Algebra Examples

Through

(9, - 8)

$(9, - 8)$ , perpendicular to

x + y = 7

$x + y = 7$

Step 1

Subtract

x

$x$ from both sides of the equation.

y = 7 - x

$y = 7 - x$

Step 2

Find the slope when

y = 7 - x

$y = 7 - x$ .

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

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 2.1.2

Reorder

7

$7$ and

- x

$- x$ .

y = - x + 7

$y = - x + 7$

y = - x + 7

$y = - x + 7$

Step 2.2

Using the slope-intercept form, the slope is

- 1

$- 1$ .

m = - 1

$m = - 1$

m = - 1

$m = - 1$

Step 3

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 4

Simplify

- \frac{1}{- 1}

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

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Step 4.1

Divide

1

$1$ by

- 1

$- 1$ .

m_{perpendicular} = 1

$m_{perpendicular} = 1$

Step 4.2

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

m_{perpendicular} = 1

$m_{perpendicular} = 1$

m_{perpendicular} = 1

$m_{perpendicular} = 1$

Step 5

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

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Step 5.1

Use the slope

1

$1$ and a given point

(9, - 8)

$(9, - 8)$ 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 - (- 8) = 1 \cdot (x - (9))

$y - (- 8) = 1 \cdot (x - (9))$

Step 5.2

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

y + 8 = 1 \cdot (x - 9)

$y + 8 = 1 \cdot (x - 9)$

y + 8 = 1 \cdot (x - 9)

$y + 8 = 1 \cdot (x - 9)$

Step 6

Solve for

y

$y$ .

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Step 6.1

Multiply

x - 9

$x - 9$ by

1

$1$ .

y + 8 = x - 9

$y + 8 = x - 9$

Step 6.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 6.2.1

Subtract

8

$8$ from both sides of the equation.

y = x - 9 - 8

$y = x - 9 - 8$

Step 6.2.2

Subtract

8

$8$ from

- 9

$- 9$ .

y = x - 17

$y = x - 17$

y = x - 17

$y = x - 17$

y = x - 17

$y = x - 17$

Step 7