How do graphs represent information? In what ways are looking at graphs easier than reading data? Why would looking at graphing relationships (the way one thing relates to another) be important? Why do we use formulas?

Graphing and Formulas

Graph: a diagram that shows a relationship between two sets of numbers Graphing Graph: a diagram that shows a relationship between two sets of numbers The x-axis runs horizontally (left- right) through zero

Independent variable (x-axis): a variable that determines the value of another variable-Variable that is being changed ex. temp, time, amount of moisture

The y-axis runs vertically (up and down) through zero Dependent variable (y-axis): A variable whose value is determined by the independent variable (examples: growth of mold, change in temp)

Graphing Relationships 1. Direct: As one variable increases, the other also increases Example: Population vs. Pollution

2. Indirect (Inverse): As one variable increases, the other decreases A. Example: Recycling vs. Amt of Garbage

3. No Relationship: As one variable increases, the other does not change Example: Color of Shoes vs. Test Score

4. Cyclic: As one variable increases, the other change in a predictable pattern A. Example: Moon Phases

Rate of Change- ESRT PAGE 1! Definition: The speed at which a variable changes over a specific period of time Equation: Change in Field Value/Time Field Value: factor being measured, in this case, typically distance or temperature Change in Field Value= Ending Value- Starting Value

Units: meter/second, miles/hour, 0F/minute, etc The bigger the answer the faster the variable is changing Example: 30 mph vs. 55 mph

Example You are climbing a hill. You start at 25 feet and end at 75 feet. It takes you 15 minutes to climb the hill. What is your rate of change? Field Value 2: Field Value 1: Change in Time: PLUG AND CHUG!

Gradient measures the slope of an object, such as a hill Equation: Change in field value/distance Change in field value= Ending elevation-Starting elevation The denominator is the horizontal distance

Units: meter/kilometer, feet/mile, etc The bigger the number, the faster the elevation changes, the steeper the gradient (aka slope) Example: Himalayas have a steeper gradient than the Catskills

Example The bottom of Mt. Beacon has an elevation of 25 feet. The top of Mt. Beacon has an elevation of 1250 feet. The distance from the bottom of the mountain to the top is 3 miles. What is the gradient of Mt. Beacon? Field Value 2: Field Value 1: Change in Distance: PLUG AND CHUG!

In Summary… For class purposes and clarification, gradient is slope and rate of change is speed- they are interconnected variables (the steeper the slope, the faster the speed)

Video Link https://www.youtube.com/watch?v=7Ih5D9W2fO A - math calculation No notes need to be taken on this video, but watch the explanation of how this teacher solves the question.