**Middle School Number Sense Lesson 103: Finding the Slope of a Line Perpendicular to Another Line)**

This concept wraps up the four different variations of the slope questions on a number sense test. It is most closely related to the

**SlopeLineEqua**concept. It has appeared

**4 times**on this year’s tests, with a median placement at

**question # 66**.

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**Number Dojo Level: 266**

A line perpendicular to a 2nd line has a slope which is the

**negative reciprocal**of the slope of the 2nd line. So if you are given the

**slope-intercept**form of an equation:

**y = mx + b**,

**m**is the slope of the line, and

**-1/m**is the slope of any line perpendicular to the given line.

If you are given the

**standard form**of an equation:

**Ax + By = C**,

**–A/B**, and the slope of any line perpendicular to this line is

**B/A**.

**Example 1: Find the slope of a line perpendicular to y = -3x + 2. ___**

- This is written in slope-intercept form.
- The slope of this line is
**-3**, so the slope of its perpendicular is**1/3**.

**Example 2: Find the slope of a line perpendicular to 3x + 5y = -3. ___**

- This is written in standard form.
- The slope of the perpendicular line is B/A, which is
**5/3**.

**Example 3: Find the slope of a line perpendicular to y = - ½ x + 17. ___**

- This is written in slope-intercept form.
- The slope of this line is
**– ½**, so the slope of its perpendicular is**2**.

**Example 4: The slope of a line perpendicular to 3x – 4y = 7 is ___**

- This is written in standard form.
- The slope of the perpendicular line is B/A, which is
**-4/3**.

**Example 5: Find the slope of a line perpendicular to 3x – 0.5 y = 7 is ___**

- This is written in standard form.
- The slope of the perpendicular line is B/A, which is
**-0.5/3**, which is**-1/6**.

**Up Next for Middle School: Parabola**