5.1: Rate of Change and Slope.  Rate of change: Shows the relationship between two VARIABLE quantities.

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Presentation transcript:

5.1: Rate of Change and Slope

 Rate of change: Shows the relationship between two VARIABLE quantities.

The table shows the elevation of a hang glider over time. Is the rate of change in elevation with respect to time constant? What does the rate of change represent? Time ( in min) Elevation (in feet) td

In words: THE HANG GLIDER’S ELEVATION FALLS 35 ft. FOR EVERY 1 min. In General: The rate of change is the ratio of the VERTICAL change to the HORIZONTAL change.

Slope is the RATIO of the CHANGE in y-values over the change in x-values. The change in y-values is called the RISE. The change in x-values is called the RUN.

 The SIGN of rise and run is very important!  Left to right and bottom to top are both POSITIVE.  Right to left and top to bottom are both NEGATIVE.

A B C D E F AB _________ CD _________ EF _________ Example - Find the slope of the following lines by counting the squares: G H GH _________

The slope of a horizontal line is ALWAYS ZERO. The slope of a vertical line is ALWAYS UNDEFINED.

Example 2– Find the slope for each of the given lines: 1). Rise of 6, run of 2 _____________ 2.) Rise of -1, run of 7 _____________

Example 3– Find the slope for each line passing through the given points: 1). A (9, 6), B (1, 4) _____________ 2.) A (-3, 1), B (2, 6) _____________ 3). A (0, 2), B (3, 0) _____________ 4.) A (10, 4), B (7, 4) _____________

Homework: 5.1 p #’s 6-40 even