April 6, 2011 - Graphing

A Maths Dictionary for Kids

What is linearity?  The study of lines.

• Directionality
• Ordered Pairs
• Graph
• Equation

Linear

Coordinate Plane

Quadrants of Coordinate Planes

Ordered Pairs

Slopes

• Slope (or rate of change) - the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.  
• Slope = rise/run (rise over run)
• always treat slope in the simplest form

Types of Slopes:

Positive slope - rises left to right

Negative slope - goes down - left to right

Zero slope - never rises, never a change in y

Undefined slope - perfectly up and down line  - x never changes
Always in the form of x = 

Examples:

3/2 (think fraction)

4/3

-2/5

-3 or -3/1

Slope Triangle

The red line is the slope I am starting with.  The white lines are helping me determine the slope.

Up 3 over 3 = 3/3...or in simplest for 1/1

Up 2 over 3 = 2/3

Negative slope
Down 4 over 5 = -4/5

The slope is 3/4.  The red and blue lines represent the slope triangle.

Formula for the slope intercept of a line  

• y = mx + b 
• the m represents the slope - how fast that line is changing
• y and x are the variables
• b = y intercept
• intercept is when a line crosses the axis. The y intercept is where the line crosses the y axis

Drawing Slopes

If your slope has a negative like - 3/5....assume that the numerator (in this case the 3)
is the negative #.  You could assume that the 5 is negative number....if you
do, you will get the same slope.

Stories to graphs

Using Coordinates to determine slope