# Why is slope of perpendicular lines?

**Perpendicular Lines**and Their

**Slopes**

**slopes**of two

**perpendicular lines**are negative reciprocals of each other. This means that if a

**line**is

**perpendicular**to a

**line**that has

**slope**m, then the

**slope**of the

**line**is -1 / m. For example, we found that the

**slope**of the

**line**y = (1/2)x + 3 is 1/2.

Similarly, you may ask, what is the slope of a perpendicular line?

Correct answer: Therefore, the **slope** of the original **line** is 1/2. A **line perpendicular** to another has a **slope** that is the negative reciprocal of the **slope** of the other **line**. The negative reciprocal of the original **line** is –2, and is thus the **slope** of its **perpendicular line**.

Furthermore, is the slope of a perpendicular line opposite? It doesn't matter what the y-intercepts are, **lines** are **perpendicular** as long their **slopes** are **opposite** reciprocals of one another. **Perpendicular lines** have **opposite** reciprocal **slopes**. Both these **lines** have reciprocal **slopes** to the **slope** of 7 in the original equation, but only the first **line** is the **opposite** reciprocal.

Also, why are the slopes of perpendicular lines negative reciprocals?

In the coordinate plane, all vertical **lines** are parallel to the y-axis and all horizontal **lines** are parallel to the x-axis. These **lines** are **perpendicular** since their **slopes** are **negative reciprocals**. The **negative reciprocal** of 2 is . If you multiply a **slope** times its **negative reciprocal**, the result is always -1.

How do you prove that two lines are perpendicular using slope?

**Two lines are perpendicular** if and only if their **slopes** are negative reciprocals. To find the **slope**, we must put the equation into **slope**-intercept form, , where equals the **slope** of the **line**. We begin by subtracting from each side, giving us . Next, we subtract 32 from each side, giving us .