lecture56 - Math 110 FS 2008 CH.2.1-2.3 3.3 Lines and...

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Math 110 FS 2008 Lectures ##5- 6. CH.2.1-2.3, 3.3. Lines and Slopes. Linear Regression. Plotting Points in the Rectangular Coordinate System. Graphs of Equations. Each point in the rectangular coordinate system corresponds with an ordered pair of real numbers ( 29 , x y . A relationship between two quantities can be expressed as an equation in two variables, such as 2 3 5, 3 6 y x y x x = - = - + The graph of the equation is the set of all points whose coordinates satisfy the equation. Graphs of Linear Equations. Use your graphing utilities to sketch graphs of , 2 , 3 , 2 y x y x y x y x = = = = - Conclusion about meaning of the parameter m : 1
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Math 110 FS 2008 Lectures ##5- 6. CH.2.1-2.3, 3.3. Lines and Slopes. Linear Regression. Use your graphing utilities to sketch graphs of , 2. 2 y x y x y x = = + = - Conclusion about meaning of the parameter b : The slope of a line. An important characteristics of a line is the angle that the line makes with the x -axis. The measure of the steepness of a line is called the slope. Slope compares the vertical change ( the rise ) to the horizontal change ( the run ) encountered when moving from one fixed point to another along the line. 2 Definition. If a line passes through two distinct points ( 29 1 1, 1 P x y and ( 29 2 2, 2 P x y , then its slope is given by the formula ( 29 ( 29 2 1 1 2 2 1 Rise vertical change m Run horizontal change y y x x x x = - = - Run Rise ( 29 1 1 1 , P x y ( 29 2 2 2 , P x y ( 29 2 1 , x y
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Math 110 FS 2008 Lectures ##5- 6. CH.2.1-2.3, 3.3. Lines and Slopes. Linear Regression. Meaning of Slope. Slope of a line is vertical shift per a unit of horizontal shift (rate of change for the linear function.) Values of slopes and interpretations.
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