Lesson 4.6

Qualitative Graphs

Sometimes the shape tells a better story than the numbers. Up, down, steady, or fast—reading the flow of the graph.

Introduction

A Qualitative Graph describes a situation without using specific numbers. It focuses on the general behavior: is it increasing? Decreasing? Is the change happening quickly (steep) or slowly (shallow)?

Past Knowledge

Lesson 4.1 (Reading Axes). Understanding what "Up" and "Right" actually mean.

Today's Goal

Interpret the shape of a graph to tell a story about speed, distance, or volume.

Future Success

This is the conceptual basis for "Derivatives" in Calculus (rates of change).

Key Concepts

The Language of Slope

INCREASING

Going Up from Left to Right.

"Gaining"

DECREASING

Going Down from Left to Right.

"Losing"

CONSTANT

Horizontal Line.

"Steady / Paused"

NON-LINEAR

Curved Line.

"Accelerating"

Worked Examples

Example 1: The Commute Story

Basic

Describe the Distance from Home.

Part A: Steep line up. Moving away from home quickly (Driving).
Part B: Horizontal line. Distance isn't changing. (Stopped at a light).
Part C: Shallow line up. Moving away slowly (School zone).
Part D: Line goes down. Distance decreases. (Returning home).

Example 2: Filling the Vase

Intermediate

Water is poured into a vase that is wide at the bottom and narrow at the top. Graph Height vs Time.

Analysis

At first, the vase is wide, so the water level rises slowly (Shallow slope).

Later, the vase is narrow, so the water level shoots up quickly (Steep slope).

Example 3: The Flag Pole

Advanced

A flag is raised up a pole, stops at the top, then is lowered jerkily (stuck, then down, stuck, then down).

Up Steady: Constant slope up.

Stop: Flat line at top.

Down/Stuck: Steps going down (Stairs).

Common Pitfalls

Speed vs Distance

A "Constant Speed" results in an "Increasing Distance" line. Students often try to draw a horizontal line for constant speed. Horizontal means stopped on a Distance graph.

Going Back in Time

You can never have a line go to the left. That would mean time travel. Graphs always move right.

Real-Life Applications

Economics: Qualitative graphs are huge in business. Executives want to see "Revenue is increasing quickly" or "Costs are leveling off" without needing to see the exact penny amount every day. The trend is more important than the data point.