1 / 9

Equations of Lines

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 2.

floyd
Download Presentation

Equations of Lines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Equations of Lines Chapter 1Seciton4

  2. 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.

  3. 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). Example 1 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.

  4. 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?

  5. Example 4: Write the equations of the lines that pass thru the point (-1,5) and have • Slope of 0 • Undefined slope Vertical and Horizontal Lines 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.

  6. 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. Parallel and Perpendicular Lines 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

  7. 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 Average Rate of Change for any Function General Form GeneralForm: 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) .

  8. 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. ?

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

More Related