Lesson 5.4

Slope from a Table

Patterns hide in plain sight. By looking at how the numbers change, we can find the slope without even graphing.

Introduction

A table is just a list of points. To find the slope, we look for the Rate of Change—how much the -value changes for every step in the -value.

Past Knowledge

Lesson 5.3 (Slope Formula). We are doing the same subtraction (), just vertically.

Today's Goal

Calculate slope from a table by finding .

Future Success

Recognizing constant rates of change is how you identify Linear Functions vs. Exponential Functions later on.

Key Concepts

The "Delta" Method

Look at the jumps between rows.

x	y
1	5
2	7
3	9

+2+2

+1+1

Change in Y over Change in X

Note:

(Delta) is a Greek letter meaning "Change".

Worked Examples

Example 1: Uniform Jumps

Basic

x	y
0	4
1	7
2	10
3	13

Find the slope.

Step 1: Change in Y

From 4 to 7 is +3.

From 7 to 10 is +3.

Step 2: Change in X

From 0 to 1 is +1.

Example 2: Negative and Big Jumps

Intermediate

x	y
2	20
4	14
6	8

Find the slope (Watch the X's!)

Step 1: Change in Y

20 to 14 goes DOWN by 6. -6.

Step 2: Change in X

2 to 4 goes UP by 2. +2.

Don't assume it's 1!

Example 3: Verifying Linearity

Advanced

x	y
1	2
3	6
5	10

Check All Jumps

Jump 1: .

Jump 2: .

The rate is constant, so it IS a line.

Common Pitfalls

Ignoring Delta X

Students just look at the Y column and say slope is the difference. This only works if X steps by 1. Always check the X side!

Inconsistent Tables

If one jump gives a slope of 2 and another gives 3, it's not a line (or you made a math error). Check multiple rows.

Real-Life Applications

Paychecks: Calculate your wage.

Hours (x)	Pay (y)
10	$150
20	$300

Change in Pay ($150) / Change in Hours (10) = $15/hour.