Learning Objectives
- Read and interpret bar graphs, pie charts, histograms, and line graphs
- Understand the Cartesian coordinate system
- Plot points on a coordinate plane
- Draw and interpret linear graphs
Key Concepts
Types of Graphs
Bar Graph: Uses bars of uniform width to represent discrete data. Bars can be vertical or horizontal with equal spacing.
Pie Chart: A circle divided into sectors representing proportions of data.
Histogram: A bar graph for continuous grouped data where bars touch each other (no gaps).
Line Graph: Data points connected by straight line segments. Useful for showing trends over time (e.g., temperature changes, stock prices).
The Coordinate System
The Cartesian plane consists of two perpendicular number lines: the x-axis (horizontal) and y-axis (vertical). They intersect at the origin O(0, 0).
Every point on the plane is represented as an ordered pair (x, y), where x is the horizontal distance and y is the vertical distance from the origin.
Quadrants
- Quadrant I: x > 0, y > 0 (both positive)
- Quadrant II: x < 0, y > 0
- Quadrant III: x < 0, y < 0 (both negative)
- Quadrant IV: x > 0, y < 0
Linear Graphs
A graph is linear if the plotted points form a straight line. Linear relationships follow the form y = mx + c, where m is the slope and c is the y-intercept.
Examples of linear relationships:
- Distance vs. time at constant speed
- Cost vs. quantity at fixed rate
- Conversion between units (e.g., Celsius to Fahrenheit)
Reading Graphs
From a graph, you can determine: (1) the value of one variable given the other, (2) trends (increasing, decreasing, constant), and (3) the rate of change.
Summary
Graphs provide visual representation of data. Different types of graphs are used for different kinds of data. The Cartesian coordinate system uses ordered pairs (x, y) to locate points. Linear graphs represent proportional or linear relationships and form straight lines on the coordinate plane.
Important Terms
- Origin: The point (0, 0) where the x-axis and y-axis intersect
- Coordinates: An ordered pair (x, y) that locates a point on the plane
- x-axis: The horizontal number line in the coordinate plane
- y-axis: The vertical number line in the coordinate plane
- Linear Graph: A graph that forms a straight line
- Quadrant: One of the four regions of the coordinate plane
Quick Revision
- Cartesian plane: x-axis (horizontal) and y-axis (vertical) meet at origin (0,0)
- Points are written as (x, y) — x first, then y
- Four quadrants: I (+,+), II (-,+), III (-,-), IV (+,-)
- Linear graphs form straight lines; represent y = mx + c
- Line graphs show trends over time
- Choose the right graph type: bar (discrete), histogram (continuous), line (trends), pie (proportions)