Notes P.4 – Lines in the Plane

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Presentation transcript:

Notes P.4 – Lines in the Plane

I. Slope: Def. – The slope of a nonvertical line through the points (x1, y1) and (x2, y2) is If the line is vertical, the slope is undefined.

II. Forms of Linear Equations: A. Point-Slope Form: B. Slope-Intercept Form: C.) General Form:

D. Vertical Line: E. Horizontal Line:

III. Linear Regression: A. Def. – The process of using data to determine a linear model or relationship between two variable quantities. B. Ex. – Determine the linear relationship between Fahrenheit and Celsius temperature. Then, find the Celsius equivalent of 90̊ F and the Fahrenheit equivalent of -5 ̊ C.

Solution: First, we provide ourselves with a linear equation to model the relationship of Now, use the fact that water boils at 100̊ C and 212 ̊ F and freezes at 0 ̊ C and 32 ̊ F to set up a system of two equations and two variables.

Solution cont.: Solving the second equation leaves us with Using substitution, we find that Therefore,

Solution cont.: When F =90 ̊ , When C =-5 ̊ ,

IV. Linear Regression with TI-83+ A. Enter the following data on your calculator and follow along with the TI-83+ overhead.

World Population in millions: Year Population 1980 4454 1985 4853 1990 5285 1995 5696 2003 6305 2004 6378 2005 6450

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Homework: p.36 #5,9,13,17,21,25,29,35,43,47,51,55,59,61-68