171S1.3q Linear Functions, Slope, and Applications January 10, 2013 Mathematica Interactive Figures are available through Tools for Success, Activities and Projects in CourseCompass. You may access these through CourseCompass or from the Important Links webpage. You must Login to MML to use this link. MAT 171 Dr. Claude Moore, CFCC Section 1.3 Linear Functions, Slope, and Applications GeoGebra Programs for Mathematics Courses http://cfcc.edu/mathlab/geogebra/ Linear Function: Graph Two Points This shows the linear functon with Graph, Slope, Yintercept, and Slopeintercept form Equation created from two points. Click on button on slider to highlight it and use left or right arrow to change value. This changes the values of (x1, y1) and (x2, y2) to construct graph and equation. Hold down the Shiftkey and use the mouse to move the grid for a better view if necessary. Click the recycle icon to reset the graph and values. Calculate the Slope, Yintercept, and write the Equation before viewing answer. Section 1.3 Slope between Two Points Section 1.3 Equations of Lines: Slope–Intercept Aug 197:45 AM Aug 229:59 PM 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. 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. If m = 1 and b = 0, the function is the identity function f (x) = x. GeoGebra Programs for Mathematics Courses are available at http://cfcc.edu/mathlab/geogebra/ Copyright © 2009 Pearson Education, Inc. Access the GeoGebra program to graph line given the slope m and the yintercept b by clicking the globe in the lowerleft corner. Jan 126:37 PM Jan 52:15 PM Average Rate of Change Example Construction laws regarding access ramps for the disabled state that every vertical rise of 1 ft requires a horizontal run of 12 ft. What is the grade, or slope, of such a ramp? 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 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. slope = (55 - 6) / (2007 - 1999) The grade, or slope, of the ramp is 8.3%. Copyright © 2009 Pearson Education, Inc. = 49 / 8 = 6.125 So, average rate of change is 6.125% per year. Jan 52:15 PM Jan 126:44 PM 1 171S1.3q Linear Functions, Slope, and Applications January 10, 2013 Section 1.3 Linear Functions, Slope, and Applications 102/2. In Exercises 14, the table of Section 1.3 Linear Functions, Slope, and Applications Find the slope of the line containing the given points. data contains input output values for a function. Answer the following questions for each table. “The grapher applet gives a simple graphing window with easy control over the viewing window.” 102/6. 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? Find the slope of the line containing the given points. 102/8. In Exercises 14, the table of data contains input output values for a function. Answer the following questions for each table. “The grapher applet gives a simple graphing window with easy control over the viewing window.” 102/4. 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? Aug 197:45 AM Aug 197:45 AM Section 1.3 Linear Functions, Slope, and Applications Find the slope of the line containing the given points. 102/16. Use the Linear Function Graph 2pts to construct graph of the lines and find the slope. Section 1.3 Linear Functions, Slope, and Applications Find the slope of the line containing the given points. 103/26. Find the slope of the line containing the given points. 102/20. 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. 103/28. Aug 197:45 AM Section 1.3 Linear Functions, Slope, and Applications 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 103/32. find the slope. Determine the slope, if it exists, of the graph of the given linear equation. Use the Linear Function Graph mb 103/34. to construct graph of the lines and find the slope. Aug 197:45 AM Use the Linear Function Graph 2pts to construct graph of the lines and find the slope. Use the Linear Function Graph 2pts to construct graph of the lines and find the slope. Aug 197:45 AM Section 1.3 Linear Functions, Slope, and Applications 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. 103/38. x = 8 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. 103/40. Aug 197:45 AM 2 171S1.3q Linear Functions, Slope, and Applications Section 1.3 Linear Functions, Slope, and Applications 104/52. Find the slope and the y intercept of the line with the given equation: y = 4 / 7. January 10, 2013 Section 1.3 Linear Functions, Slope, and Applications 104/62. Find the slope and the yintercept of the line with the given equation: f(x) = 0.3 + x Use the Linear Function Graph abc to construct graph of the lines and find the slope. 104/56. 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. Aug 197:45 AM Section 1.3 Linear Functions, Slope, and Applications 104/72. 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]. 104/68. Graph equation using the slope and the Use the Linear Function Graph yintercept: 2x + 3y = 15 abc to construct graph of the lines and find the slope. Aug 197:45 AM Section 1.3 Linear Functions, Slope, and Applications 104/?. 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. Average rate of change = 1.915 million HIV cases per year Aug 197:45 AM Aug 197:45 AM Section 1.3 Linear Functions, Slope, and Applications Section 1.3 Linear Functions, Slope, and Applications 104/??. 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. 105/???. 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). NOTE: 1 atm = 14.5 psi P(0) = 1.0 atm = 14.5 psi P(5) = 1.2 atm = 16.7 psi P(10) = 1.3 atm = 18.9 psi P(33) = 2.0 atm = 29 psi P(100) = 4.0 atm = 58 psi Aug 188:10 PM Aug 197:45 AM 3
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