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1.4 Equations of Lines and Linear Models Quiz If two distinct lines, y=m1x+b1, y=m2x+b2 , are parallel with each other, what’s the relationship between m1 and m2? Point-Slope Form Given the slope m of a linear function and a point (x1,y1) on the graph of the linear function. We write the equation of the linear function as y-y1=m(x-x1) We call a linear equation in this form as point-slope form of a linear function. Standard Form A linear equation written in the form Ax+By=C, where A,B, and C are real numbers(A and B not both 0), is said to be in standard form. Notice:When A≠0, B=0, the linear equation will be Ax=C, which is a vertical line and is not a linear function. Point-Slope Form Exercise: Write the equation of the line through (-1,3) and (-2,-3). Does it matter which point is used? Parallel and Perpendicular Lines Parallel Lines: Two distinct non-vertical lines are parallel if and only if they have the same slope. y y=m2x+b2 y=m1x+b1 x m1=m2 Parallel and Perpendicular Lines Perpendicular Lines: Two lines, neither of which is vertical, are perpendicular if and only if their slopes have product -1 y=m2x+b2 y y=m1x+b1 x m1 × m2=-1 Parallel and Perpendicular Lines Exercises: 1, Write the equation of the line through (-4,5) that is parallel to y=(1/2)x+4 2, Write the equation of the line through (5,-1) that is perpendicular to 3x-y=8. Graph both lines by hand and by using the GC. 3, Write the equation of the line through (2/3,3/4) that is perpendicular to y=1. Graph both lines by hand and by using the GC. Linear Applications Example 1: The cellular Connection charges $60 for a phone and $29 per month under its economy plan, Write an equation that can model the total cost, C, of operating a Cellular Connection phone for t months. Find the total cost for six months. Linear Application Example 2: The number of land-line phones in the US has decreased from 101 million in 2001 to 172 million in 2006. What is the average rate of change for the number of land-line phones over that time? Predict how many land-line phones are in use in 2010. Linear Regression Why Linear Regression? In most real-life situations data seldom fall into a precise line. Because of measurement errors or other random factors, a scatter plot of real-world data may appear to lie more or less on a line, but not exactly. Fitting lines to data is one of the most important tools available to researchers who need to analyze numerical data. Linear Regression http://www.youtube.com/watch?v=nw6G OUtC2jY&feature=related Linear Regression Example 1: US infant mortality Year Rate 1950 29.2 1960 26.0 1970 20.0 1980 12.6 1990 9.2 2000 6.9 1, Find the regression line for the infant mortality data. 2, Estimate the infant mortality rate in 1995. 3, Predict mortality rate in 2006. Homework PG. 42: 5-60(M5); 61, 63, 65, Supplement(linear Regression) KEY: 20, 45, 50, 63, S: 3, 5 Reading: 1.5 Solving Equation & Inequalities