Linear Functions Notes and Worksheets - Lindsay Bowden - Free Printable

Problem Analysis:

The image is a worksheet titled "Slope Notes," which aims to teach students about the concept of slope in linear graphs. The worksheet includes definitions, types of slopes, and methods for finding slope from a graph. Below, I will fill in the blanks and explain each part step by step.

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Section 1: Slope Definition

#### Filling in the blanks:
1. slope - the _______ of _______ on a linear graph
- Answer: slope - the steepness of a line on a linear graph

2. slope has many definitions:
- the change in ______ over the change in ______
- Answer: the change in y over the change in x
- \(\frac{\Delta y}{\Delta x}\) (delta) means _______
- Answer: \(\Delta\) (delta) means change in
- _______ over _______
- Answer: rise over run
- the _______ of a line
- Answer: the direction of a line

3. the letter ______ represents slope
- Answer: the letter m represents slope

4. slope is written as a _______ in simplest form
- Answer: slope is written as a fraction in simplest form

5. slope is an important part of _______ functions and will help us with _______ and solving _______ problems
- Answer: slope is an important part of linear functions and will help us with graphing and solving real-world problems

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Section 2: Types of Slope

The worksheet provides four types of slopes with corresponding diagrams and descriptions:
1. Positive Slope: \( m = \text{positive number} \)
- The line goes up as you move from left to right.
2. Negative Slope: \( m = \text{negative number} \)
- The line goes down as you move from left to right.
3. Zero Slope: \( m = 0 \)
- The line is horizontal.
4. Undefined Slope: \( m = \text{undefined} \)
- The line is vertical (happens when dividing by 0).

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Section 3: Finding Slope from a Graph

#### Filling in the blanks:
1. We can find the slope of a graphed line by counting the ______ over ______.
- Answer: We can find the slope of a graphed line by counting the rise over run.

#### Examples:
The worksheet provides three graphs to practice finding the slope. Let's calculate the slope for each:

1. Graph 1:
- Points: \((-4, 4)\) and \((4, -4)\)
- Rise: \(\Delta y = -4 - 4 = -8\)
- Run: \(\Delta x = 4 - (-4) = 8\)
- Slope: \( m = \frac{\Delta y}{\Delta x} = \frac{-8}{8} = -1 \)

2. Graph 2:
- Points: \((-1, -1)\) and \((1, 1)\)
- Rise: \(\Delta y = 1 - (-1) = 2\)
- Run: \(\Delta x = 1 - (-1) = 2\)
- Slope: \( m = \frac{\Delta y}{\Delta x} = \frac{2}{2} = 1 \)

3. Graph 3:
- Points: \((0, 2)\) and \((0, -2)\)
- Rise: \(\Delta y = -2 - 2 = -4\)
- Run: \(\Delta x = 0 - 0 = 0\)
- Slope: \( m = \frac{\Delta y}{\Delta x} = \frac{-4}{0} \) (undefined)

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Final Answer:

\[
\boxed{
\text{steepness, line, y, x, change in, rise, run, direction, m, fraction, linear, graphing, real-world, rise, run, -1, 1, undefined}
}
\]