MAT 171 Linear Functions - Success starts...
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171S1.3 Linear Functions, Slope, and Applications 1 August 19, 2011 MAT 171 Dr. Claude Moore, CFCC Section 1.3 Linear Functions, Slope, and Applications • WebAdvisor: http://reg.cfcc.edu 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). Click the globe in lowerleft corner. Dr. Moore 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: • myCFCC : http://my.cfcc.edu Click the globe in lowerleft corner. 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. Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. Example The grade, or slope, of the ramp is 8.3%. Construction laws regarding access ramps for the disabled state that every vertical rise of 1 ft requires a horizontal run of 12 ft.
Transcript of MAT 171 Linear Functions - Success starts...
171S1.3 Linear Functions, Slope, and Applications
1
August 19, 2011
MAT 171 Dr. Claude Moore, CFCCSection 1.3 Linear Functions, Slope, and Applications
• WebAdvisor: http://reg.cfcc.edu
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). Click the globe in lowerleft corner.
Dr. Moore
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:• myCFCC : http://my.cfcc.edu Click the globe in lowerleft corner.
Linear FunctionsA 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.
Copyright © 2009 Pearson Education, Inc.
Applications of SlopeThe 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.
Copyright © 2009 Pearson Education, Inc.
Example
The grade, or slope, of the ramp is 8.3%.
Construction laws regarding access ramps for the disabled state that every vertical rise of 1 ft requires a horizontal run of 12 ft.
171S1.3 Linear Functions, Slope, and Applications
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August 19, 2011
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.
Average Rate of Change
The percent of travel bookings online has increased from 6% in 1999 to 55% in 2007. The graph below illustrates this trend. Find the average rate of change in the percent of travel bookings made online from 1999 to 2007.
Example
Section 1.3 Linear Functions, Slope, and Applications 110/2.
110/4.
In Exercises 14, 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?
Section 1.3 Linear Functions, Slope, and Applications
110/6.
110/8.
Find the slope of the line containing the given points. “The grapher applet gives a simple graphing window with easy control over the viewing window.”
171S1.3 Linear Functions, Slope, and Applications
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Section 1.3 Linear Functions, Slope, and Applications
111/16.
111/20.
Find the slope of the line containing the given points. Use the Linear Function Graph 2pts to construct graph of the lines and find the slope.
Section 1.3 Linear Functions, Slope, and Applications
111/26.
111/28.
Find the slope of the line containing the given points.
Section 1.3 Linear Functions, Slope, and Applications
111/32.
111/38.
Determine the slope, if it exists, of the graph of the given linear equation.Use the Linear Function Graph mb to construct graph of the lines and find the slope.
Section 1.3 Linear Functions, Slope, and Applications
111/40. 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 2005. 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 2005.
171S1.3 Linear Functions, Slope, and Applications
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112/44.
Section 1.3 Linear Functions, Slope, and Applications
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 2006.
Section 1.3 Linear Functions, Slope, and Applications
112/50. Find the slope and the y intercept of the line with the given equation: y = 4 / 7.
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 lines and find the slope.
Section 1.3 Linear Functions, Slope, and Applications
112/60. Find the slope and the yintercept of the line with the given equation: f(x) = 0.3 + x
Section 1.3 Linear Functions, Slope, and Applications
113/66. Graph equation using the slope and the yintercept: 2x + 3y = 15
171S1.3 Linear Functions, Slope, and Applications
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Section 1.3 Linear Functions, Slope, and Applications
113/70. 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.
b) Find P(0), P(5), P(10), P(33), and P(100).
Section 1.3 Linear Functions, Slope, and Applications
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].
Section 1.3 Linear Functions, Slope, and Applications113/74. StraightLine 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 tradein, or salvage, value will be $ 1100. 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) = 5200 512.50t, 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.
