Equations of Lines Chapter 1Seciton4

Forms for the Equation of a Line Slope-Intercept form: m is the slope(rate of change) and b is the y-intercept (initial value when x = 0). Point-Slope form: m is the slope and is a known point.

Example 1 Example 2 Write an equation for the line passing thru (-1,5) and has a slope of ¾ . Write the equation of the line passing thru (-1,5) and (2,4). Appliance Repair An appliance repairman charges $60 for a service call plus $25 per hr for each hour spent on the repair. Assuming his service call charges can be modeled by a linear function of hours spent on the repair, write the equation of the function.

Example 3 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 2000. What is the rate of growth of people incarcerated from 1990 to 2000? Write a linear function that models the number of N, prisoners as a function of the year x. The Bureau of Justice Statistics projected that 2.29 million people would be incarcerated in 2005. Does the model agree with this projection?

Vertical and Horizontal Lines Example 4: Write the equations of the lines that pass thru the point (-1,5) and have Slope of 0 Undefined slope A vertical line has the form x = a, where a is a constant and the coordinate of any point on the line. A horizontal line has the form y = b where b is a constant and the coordinate of any point on the line.

Parallel and Perpendicular Lines Example 5 Write the equation of the line through (4,5) and Parallel to the line with equation 3x + 2y = -1. Perpendicular to the line with equation 3x + 2y = -1. Two distinct non-vertical lines that have the same slope are called parallel. If Line, L1 has slope m1 and Line, L2 has slope m2, then The slopes of perpendicular lines are negative reciprocals of each other. If Line, L1 has slope m1 and Line, L2 has slope m2, then

General Form Average Rate of Change for any Function General Form: Ax + By = C and A,B,C are whole numbers and A is positive. The slope, m = -A/B and the intercepts are (0, C/B ) and ( C/A, 0) . The average rate of change of f(x) with respect to x over the interval from x = a to x = b (moving left to right) is calculated as Average rate of change = Change in f(x) values change in x values

Example 6: Hybrid Vehicle Sales The total hybrid electric passenger vehicle sales for the years from 1997 to 2005 are shown in the figure. The number of sales can be modeled by the function where S(x) is in thousands and x is in years after 1990. Find the average rate of change between 2000 and 2006. Interpret your answer. Find the slope of the secant line joining the points (10, 12.692) and (16, 264.710). How does that compare to part a. ?

Difference Quotient Example 7 The average rate of change of the function f(x) from x to x + h is