Finite Math Examples

$y = x$ , $(1, 3)$

Step 1

Use the slope-intercept form to find the slope.

Tap for more steps...

Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is $1$ .

$m = 1$

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

Cancel the common factor of $1$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Multiply $- 1$ by $1$ .

$m_{perpendicular} = - 1$

Step 4

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

Tap for more steps...

Step 4.1

Use the slope $- 1$ and a given point $(1, 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = - 1 \cdot (x - (1))$

Step 4.2

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

$y - 3 = - 1 \cdot (x - 1)$

Step 5

Solve for $y$ .

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Rewrite.

$y - 3 = 0 + 0 - 1 \cdot (x - 1)$

Step 5.1.2

Simplify by adding zeros.

$y - 3 = - 1 \cdot (x - 1)$

Step 5.1.3

Apply the distributive property.

$y - 3 = - 1 x - 1 \cdot - 1$

Step 5.1.4

Simplify the expression.

Tap for more steps...

Step 5.1.4.1

Rewrite $- 1 x$ as $- x$ .

$y - 3 = - x - 1 \cdot - 1$

Step 5.1.4.2

Multiply $- 1$ by $- 1$ .

$y - 3 = - x + 1$

Step 5.2

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 5.2.1

Add $3$ to both sides of the equation.

$y = - x + 1 + 3$

Step 5.2.2

Add $1$ and $3$ .

$y = - x + 4$

Step 6