Question

name:
topic:
date:
class:
main ideas/questions
notes/examples
rate of change
on a linear graph, this is called the ____________ of the line!
slope

• slope is written as a ______ of the vertical change (___) to the horizontal change (_____) between any two points on a line.
• this remains _____________ for any two points on the same line.
• slope is written as a __________ in ________ _____
• variable for slope: ______

types of slope
finding slope on a graph
m =
directions: find the slope of each line. write your answer in simplest form!
1.
2.
3.
4.

Explanation:

Problem 1:

Step 1: Identify two points

Let's take the origin \((0,0)\) and another point, say \((4,4)\) (by counting the grid).

Step 2: Calculate vertical and horizontal change

Vertical change (\(rise\)): \(4 - 0 = 4\)
Horizontal change (\(run\)): \(4 - 0 = 4\)

Step 3: Find slope (\(m=\frac{rise}{run}\))

\(m = \frac{4}{4} = 1\)

Problem 2:

Step 1: Identify two points

Take \((0, -2)\) and \((2, 2)\) (from the graph).

Step 2: Calculate rise and run

Rise: \(2 - (-2) = 4\)
Run: \(2 - 0 = 2\)

Step 3: Compute slope

\(m = \frac{4}{2} = 2\)

Problem 3:

Step 1: Identify two points

Let's use \((-4, 2)\) and \((4, 0)\).

Step 2: Find rise and run

Rise: \(0 - 2 = -2\)
Run: \(4 - (-4) = 8\)

Step 3: Calculate slope

\(m = \frac{-2}{8} = -\frac{1}{4}\)

Problem 4:

Answer:

s:

1. \(1\)
2. \(2\)
3. \(-\frac{1}{4}\)
4. \(-1\)