2QuizIf two distinct lines, y=m1x+b1, y=m2x+b2 , are parallel with each other, what’s the relationship between m1 and m2?
3Point-Slope FormGiven 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.
4Standard FormA 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.
5Point-Slope FormExercise: Write the equation of the line through (-1,3) and (-2,-3). Does it matter which point is used?
6Parallel and Perpendicular Lines Parallel Lines: Two distinct non-vertical lines are parallel if and only if they have the same slope.y=m2x+b2yy=m1x+b1m1=m2x
7Parallel and Perpendicular Lines Perpendicular Lines: Two lines, neither of which is vertical, are perpendicular if and only if their slopes have product -1yy=m2x+b2y=m1x+b1m1 × m2=-1x
8Parallel 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.
9Linear ApplicationsExample 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.
10Linear ApplicationExample 2: The number of land-line phones in the US has decreased from 101 million in 2001 to 172 million in 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.
11Linear RegressionWhy 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.
13Linear Regression Example 1: US infant mortality YearRate195029.2196026.0197020.0198012.619909.220006.91, Find the regression line for the infant mortality data.2, Estimate the infant mortality rate in 1995.3, Predict mortality rate in 2006.