Notes P.4 – Lines in the Plane

I. Slope: Def. – The slope of a nonvertical line through the points (x 1, y 1 ) and (x 2, y 2 ) 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 90 ̊ 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 100 ̊ 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.

YearPopulation World Population in millions:

V. Quick Review Complete the in-class worksheet.