**Middle School Number Sense Lesson 102: Finding the Slope of a Line Given Two Points**

This concept is similar to

**SlopeLineEqua**, but instead of calculating the slope using a linear equation, we will calculate it by using two points. These problems have shown up

**5 times**this year, with a median placement of

**question # 55**.

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I like to think of a line’s slope as the “

**rise over run**”—meaning the distance it goes up, divided by the distance it goes across. When given two points (x, y) and (X, Y), we can use this formula:

**(Y – y)**

**----------**

**(X – x)**

**: It is VERY important to keep the points in the same order, or we end up with the wrong answer.**

__Note__**Example 1: Find the slope of a line which contains the points (4, 3) and (8, 9). ___**

- Numerator: Y – y = 9 – 3 =
**6** - Denominator: X – x = 8 – 4 =
**4** - The answer is 6/4 =
**3/2**

**Example 2: Find the slope of a line passing through (-3, 7) and (6, -2). ___**

- Numerator: Y – y = -2 – 7 =
**-9** - Denominator: X – x = 6 – (-3) =
**9** - The answer is -9/9 =
**-1**

**Example 3: The slope of the line passing through (2.5, 3) and (3.5, 6) = ___**

- Numerator: Y – y = 6 – 3 =
**3** - Denominator: X – x = 3.5 – 2.5 =
**1** - The answer is 3/1 =
**3**

**Example 4: The slope of a line with x-intercept (4, 0) and passing through (7, 7) is ___**

- Numerator: Y – y = 7 – 0 =
**7** - Denominator: X – x = 7 – 4 =
**3** - The answer is
**7/3**

**Example 5: The slope of a line with x-intercept 9 and y-intercept of -4 is ___**

- The x-intercept is
**(9, 0)**, and the y-intercept is**(0, -4)**. - Numerator: Y – y = -4 – 0 =
**-4** - Denominator: X – x = 0 – 9 =
**-9** - The answer is (-4)/(-9) =
**4/9**

**Up Next for Middle School: SlopeLinePerp**