Presentation on theme: "1.4 Equations of Lines and Linear Models. Quiz If two distinct lines, y=m 1 x+b 1, y=m 2 x+b 2, are parallel with each other, what’s the relationship."— Presentation transcript:
1.4 Equations of Lines and Linear Models
Quiz If two distinct lines, y=m 1 x+b 1, y=m 2 x+b 2, are parallel with each other, what’s the relationship between m 1 and m 2 ?
Point-Slope Form Given the slope m of a linear function and a point (x 1,y 1 ) on the graph of the linear function. We write the equation of the linear function as y-y 1 =m(x-x 1 ) 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. x y y=m 1 x+b 1 y=m 2 x+b 2 m 1 =m 2
Parallel and Perpendicular Lines Perpendicular Lines: Two lines, neither of which is vertical, are perpendicular if and only if their slopes have product -1 x y y=m 1 x+b 1 y=m 2 x+b 2 m 1 × m 2 =-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 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.
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Linear Regression Example 1: US infant mortality YearRate , Find the regression line for the infant mortality data. 2, Estimate the infant mortality rate in , Predict mortality rate in 2006.