MAT 171. Linear Functions. Example. January 13, S1.3 Linear Functions, Slope, and Applications. Applications of Slope

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1 MAT 171 Dr. Claude Moore, CFCC Session 1 introduces the Course, CourseCompass, and Chapter 1: Graphs, Functions, and Models. This session is available in CourseCompass. Read the Announcements to find Session 1. If the CFCC website is not available, you may access the following with links: Campus Cruiser : WebAdvisor: I suggest that you view the examples that were not worked in your section. If you have questions or need assistance, please contact me or go to the Math Lab (S606) or the Learning Lab (L Building). Dr. Moore Linear Functions A function f is a linear function if it can be written as f (x) = mx + b, where m and b are constants. If m = 0, the function is a constant function f (x) = b. If m = 1 and b = 0, the function is the identity function f (x) = x. Graph line given m and b. Applications of Slope The grade of a road is a number expressed as a percent that tells how steep a road is on a hill or mountain. A 4% grade means the road rises 4 ft for every horizontal distance of 100 ft. Example Construction laws regarding access ramps for the disabled state that every vertical rise of 1 ft requires a horizontal run of 12 ft. The grade, or slope, of the ramp is 8.3%. Copyright 2009 Pearson Education, Inc. Copyright 2009 Pearson Education, Inc. 1

2 Average Rate of Change Slope can also be considered as an average rate of change. To find the average rate of change between any two data points on a graph, we determine the slope of the line that passes through the two points. Example The percent of travel bookings online has increased from 6% in 1999 to 55% in The graph below illustrates this trend. Find the average rate of change in the percent of travel bookings made online from 1999 to /2. In Exercises 1 4, the table of data contains input output values for a function. Answer the following questions for each table. a) Is the change in the inputs x the same? b) Is the change in the outputs y the same? c) Is the function linear? 110/4. Find the slope of the line containing the given points. 110/6. The grapher applet gives a simple graphing window with easy control over the viewing window. Find the slope of the line containing the given points. Use the Linear Function Graph 111/16. 2pts to construct graph of the 110/8. 111/20. m =

3 Find the slope of the line containing the given points. 111/26. Determine the slope, if it exists, of the graph of the given linear equation. Use the Linear Function Graph 111/32. mb to construct graph of the This is of the form y = mx + b. Therefore, m = / /38. This is of the form y = mx + b. Therefore, m = /40. HIV Cases. HIV, human immunodeficiency virus, spreads to 10 people every minute. It is estimated that there were about 40.3 million cases of HIV worldwide in The estimated number of cases in 1985 was about 2 million. ( Source: UNAIDS) Find the average rate of change in the number of adults and children worldwide with HIV from 1985 to /44. Credit Card Debt. From 1992 to 2006, the average household credit card balance has risen 172%. Use the data in the graph below to find the average rate of change in the average credit card balance from 1992 to

4 112/50. Find the slope and the y intercept of the line with the given equation: y = 4 / /60. Find the slope and the y intercept of the line with the given equation: f(x) = x 112/54. Find the slope and the y intercept of the line with the given equation: 2x 3y = 12. Use the Linear Function Graph abc to construct graph of the 113/66. Graph equation using the slope and the y intercept: 2x + 3y = /70. Pressure at Sea Depth. The function P, given by P = (1/33)d + 1, gives the pressure, in atmospheres (atm), at a depth d, in feet, under the sea. a) Graph P. b1. b) Find P(0), P(5), P(10), P(33), and P(100). b2. b3. 4

5 113/71. Stopping Distance on Glare Ice. The stopping distance (at some fixed speed) of regular tires on glare ice is a function of the air temperature F, in degrees Fahrenheit. This function is estimated by D(F) = 2F + 115, where is the stopping distance, in feet, when the air temperature is F, in degrees Fahrenheit. a) Graph D. b) Find D(0), D( 20), D(10), and D(32). c) Explain why the domain should be restricted to [ 57.5, 32]. 113/74. Straight Line Depreciation. A marketing firm buys a new color printer for $ 5200 to print banners for a sales campaign. The printer is purchased on January 1 and is expected to last 8 yr, at the end of which time its trade in, or salvage, value will be $ If the company figures the decline or depreciation in value to be the same each year, then the salvage value V, after t years, is given by the linear function V(t) = t, for 0 < t < 8. a) Graph V. b) Find V(0), V(1), V(2), V(3), and V(8). c) Find the domain and the range of this function. 5