Algebra Examples

through:

(1, - 4)

$(1, - 4)$ , perp. to

y = - x + 1

$y = - x + 1$

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

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

Divide

1

$1$ by

- 1

$- 1$ .

m_{perpendicular} = 1

$m_{perpendicular} = 1$

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

(1, - 4)

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

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

Step 4.2

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

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

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

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

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

Step 5

Solve for

y

$y$ .

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Step 5.1

Multiply

x - 1

$x - 1$ by

1

$1$ .

y + 4 = x - 1

$y + 4 = x - 1$

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

Subtract

4

$4$ from both sides of the equation.

y = x - 1 - 4

$y = x - 1 - 4$

Step 5.2.2

Subtract

4

$4$ from

- 1

$- 1$ .

y = x - 5

$y = x - 5$

y = x - 5

$y = x - 5$

y = x - 5

$y = x - 5$

Step 6