**Middle School Number Sense Lesson 66: Finding the Slope of a Line Given an Equation**

There are several different types of number sense questions where we are asked to find the slope of a line:

- Given an equation
- Given two points
- Perpendicular to the given line
- Tangent to the given equation at a certain point

**8 times**last year in middle school, with a median placement at

**question # 65**.

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You may have been taught the

**slope-intercept**form of an equation, which is:

**y = mx + b**

**m is the slope**, and b is the y-intercept (where the line crosses the y axis). If the equation is given in this form, simply write the value of

**m**.

However, the vast majority of these questions give an equation in the

**standard form**of:

**Ax + By = C**

**-A/B**.

**Example 1: Find the slope of the line 4x - 7y = 13. ___**

- The slope can be calculated as
**-A/B**. - -(4)/(-7) =
**4/7**.

**Example 2: The slope of the line 2x - y = 5 is ___**

- The slope is
**-A/B**. - -2/(-1) =
**2**.

**Example 3: If the slope of the line Ax + 4y = 18 is 1.5, then A = ___**

- The slope is
**-A/B**. - 1.5 = -A/4. Solve for A by multiplying both sides by
**-4**. **-6**= A.

Example 4: The slope of a line with equation 1/2 x - 1/3 y = 11 is ___

Example 4: The slope of a line with equation 1/2 x - 1/3 y = 11 is ___

- The slope is
**-A/B**. - -(1/2)/(-1/3) = (-1/2) x (-3/1) =
**3/2**.

**Example 5: The slope of the line y = x + 8 is ___**

- This equation is written in slope-intercept form, so the slope is the coefficient of x.
- The answer is
**1**.

Example 6: The slope of the line .7x - .9y = .4 is ___

Example 6: The slope of the line .7x - .9y = .4 is ___

- The slope is
**-A/B**. - -(.7)/(-.9) =
**7/9**.

**Check back soon for a free worksheet to help you practice SlopeLineEqua.**

**Up Next for Middle School: FindIntercept**