Equations of Lines

 The slope intercept for of the equation of a line with slope m and y-intercept b is y=mx+b. In an applied context, m is the rate of change and b is the intial value (when x=0)

 The equation of the line with slope m that passes through a known point (x 1,y 1 ) is y-y 1 = m(x-x 1 )

 A) Is the rate of change of the Blood Alcohol percent a constant? What is it?  B) Write the equation of the function that models the blood alcohol percent as a function of the number of drinks.

 Use two points to find slope.  Use point slope form with one of the points.

 The number of people (in millions) in US prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people incarcerated in 1990 and 1.91 million incarcerated in  A) What is the rate of growth of people incarcerated from 1990 to 2000?  B) Write a linear equation that models the number N prisoners as a function of the year x  C) The Bureau of Justice Statistics projected that 2.29 million people would be incarcerated in Does your model agree with this projection?

 Horizontal lines have a slope of 0.  When two points of a horizontal line are given the y values are the same.  When writing an equation for a horizontal line, it should be written as y=a

 Vertical lines have an undefined slope.  When two points of a vertical line are given the x values are the same.  When writing an equation for a vertical line, it should be written as x=a.

 Two lines are considered to be parallel if they have the exact same slope.  Use point slope form to find equation given a point and a parallel line.

 Two lines are considered to be perpendicular if they have slopes that are opposite reciprocals.  Use point slope form to find equation given point and perpendicular line.

 Ax + By = C  A,B, and C are real numbers, with A and B not both equal to 0.

 Example 8 on page 67

 Example 9 on page 68

 Pages  1,3,7-9,11,15,25,27,33,35,37,43,49,53

 Pages  1-42