Algebra Examples

(3, 5)

$(3, 5)$ ,

m = 5

$m = 5$

Step 1

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

m_{perpendicular} = - \frac{1}{5}

$m_{perpendicular} = - \frac{1}{5}$

Step 2

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

Tap for more steps...

Step 2.1

Use the slope

- \frac{1}{5}

$- \frac{1}{5}$ and a given point

(3, 5)

$(3, 5)$ 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 - (5) = - \frac{1}{5} \cdot (x - (3))

$y - (5) = - \frac{1}{5} \cdot (x - (3))$

Step 2.2

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

y - 5 = - \frac{1}{5} \cdot (x - 3)

$y - 5 = - \frac{1}{5} \cdot (x - 3)$

y - 5 = - \frac{1}{5} \cdot (x - 3)

$y - 5 = - \frac{1}{5} \cdot (x - 3)$

Step 3

Write in

y = m x + b

$y = m x + b$ form.

Tap for more steps...

Step 3.1

Solve for

y

$y$ .

Tap for more steps...

Step 3.1.1

Simplify

- \frac{1}{5} \cdot (x - 3)

$- \frac{1}{5} \cdot (x - 3)$ .

Tap for more steps...

Step 3.1.1.1

Rewrite.

y - 5 = 0 + 0 - \frac{1}{5} \cdot (x - 3)

$y - 5 = 0 + 0 - \frac{1}{5} \cdot (x - 3)$

Step 3.1.1.2

Simplify by adding zeros.

y - 5 = - \frac{1}{5} \cdot (x - 3)

$y - 5 = - \frac{1}{5} \cdot (x - 3)$

Step 3.1.1.3

Apply the distributive property.

y - 5 = - \frac{1}{5} x - \frac{1}{5} \cdot - 3

$y - 5 = - \frac{1}{5} x - \frac{1}{5} \cdot - 3$

Step 3.1.1.4

Combine

x

$x$ and

\frac{1}{5}

$\frac{1}{5}$ .

y - 5 = - \frac{x}{5} - \frac{1}{5} \cdot - 3

$y - 5 = - \frac{x}{5} - \frac{1}{5} \cdot - 3$

Step 3.1.1.5

Multiply

- \frac{1}{5} \cdot - 3

$- \frac{1}{5} \cdot - 3$ .

Tap for more steps...

Step 3.1.1.5.1

Multiply

- 3

$- 3$ by

- 1

$- 1$ .

y - 5 = - \frac{x}{5} + 3 (\frac{1}{5})

$y - 5 = - \frac{x}{5} + 3 (\frac{1}{5})$

Step 3.1.1.5.2

Combine

3

$3$ and

\frac{1}{5}

$\frac{1}{5}$ .

y - 5 = - \frac{x}{5} + \frac{3}{5}

$y - 5 = - \frac{x}{5} + \frac{3}{5}$

y - 5 = - \frac{x}{5} + \frac{3}{5}

$y - 5 = - \frac{x}{5} + \frac{3}{5}$

y - 5 = - \frac{x}{5} + \frac{3}{5}

$y - 5 = - \frac{x}{5} + \frac{3}{5}$

Step 3.1.2

Move all terms not containing

y

$y$ to the right side of the equation.

Tap for more steps...

Step 3.1.2.1

Add

5

$5$ to both sides of the equation.

y = - \frac{x}{5} + \frac{3}{5} + 5

$y = - \frac{x}{5} + \frac{3}{5} + 5$

Step 3.1.2.2

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

y = - \frac{x}{5} + \frac{3}{5} + 5 \cdot \frac{5}{5}

$y = - \frac{x}{5} + \frac{3}{5} + 5 \cdot \frac{5}{5}$

Step 3.1.2.3

Combine

5

$5$ and

\frac{5}{5}

$\frac{5}{5}$ .

y = - \frac{x}{5} + \frac{3}{5} + \frac{5 \cdot 5}{5}

$y = - \frac{x}{5} + \frac{3}{5} + \frac{5 \cdot 5}{5}$

Step 3.1.2.4

Combine the numerators over the common denominator.

y = - \frac{x}{5} + \frac{3 + 5 \cdot 5}{5}

$y = - \frac{x}{5} + \frac{3 + 5 \cdot 5}{5}$

Step 3.1.2.5

Simplify the numerator.

Tap for more steps...

Step 3.1.2.5.1

Multiply

5

$5$ by

5

$5$ .

y = - \frac{x}{5} + \frac{3 + 25}{5}

$y = - \frac{x}{5} + \frac{3 + 25}{5}$

Step 3.1.2.5.2

Add

3

$3$ and

25

$25$ .

y = - \frac{x}{5} + \frac{28}{5}

$y = - \frac{x}{5} + \frac{28}{5}$

y = - \frac{x}{5} + \frac{28}{5}

$y = - \frac{x}{5} + \frac{28}{5}$

y = - \frac{x}{5} + \frac{28}{5}

$y = - \frac{x}{5} + \frac{28}{5}$

y = - \frac{x}{5} + \frac{28}{5}

$y = - \frac{x}{5} + \frac{28}{5}$

Step 3.2

Reorder terms.

y = - (\frac{1}{5} x) + \frac{28}{5}

$y = - (\frac{1}{5} x) + \frac{28}{5}$

Step 3.3

Remove parentheses.

y = - \frac{1}{5} x + \frac{28}{5}

$y = - \frac{1}{5} x + \frac{28}{5}$

y = - \frac{1}{5} x + \frac{28}{5}

$y = - \frac{1}{5} x + \frac{28}{5}$

Step 4