Lesson 12 Section 2.3

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Stewart Jenkins
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1 Lesson Section.3 Compare the graphs of the lines below. A B C = = + 3 = How does each point of graph B compare with graph A (directl below)? How does each point of graph C compare with graph A (directl above)? If the equations of B and C are considered to be in the form = m + b, the point (0, b) represents the -intercept. The value of m represents the 'slant' of the line, called the slope. st wa to find slope vertical change slope = m = horizontal change SLOPE FORMULA: m = = rise run difference of = difference of 's 's = or nd wa to find slope

2 The vertical change (rise) can be compared to the horizontal change (run) b counting on a graph. Find the slope of each line described. 3 rd wa to find slope ) (-,-) (4,0) ) 4 5 = 0 3) points: (-, -8) and (-3, ) 4) = 3 4 5) points: (3, 0) and (-4, -0) (-,) 6) (,-)

3 Slope-Intercept Form: The form = m + b is called the slope-intercept form where m is the slope and (0, b) is the -intercept. The form f ( ) = m + b is slope-intercept form of a linear function. 3 7) Write a linear function for a line with slope and -intercept 0,. 3 8) Find the slope and -intercept. 3 = You can graph a line using the slope and -intercept. Begin on the -ais at the -intercept. Count up or down corresponding to rise, then left or right corresponding to run to find another point. Draw the line. 5 9) Use the slope and -intercept to graph the line. f ( ) =

4 5 0) g ( ) = ) Determine the slope and -intercept, then graph. 4 = 8

5 ) Graph h ( ) =

6 APPLICATIONS ) Year % of U.S. homes with multiple computers Notice: Each ear, the percent of U.S. homes with multiple computers grew b 3.6%. This is called the rate of change and is equal to the slope, if a graph was made with the -ais representing ears and -ais representing percent. a) Let t = number of ears since 997 Write appropriate data points (t, P(t)) for 997 and 00. b) Find the average rate of change from the data points. c) Write a linear function P(t) = mt + b. d) Use the linear function to predict what percent of U.S. homes had more than one computer in 005. e) Use the linear function to predict what ear the percent of homes with more than computer is about 50%. f) If this trend continues, when will all U.S. homes have more than computer?

7 ) The graph below represent the value of a computer model (in hundreds of dollars) for a number of ears after it is used. 30 value of computer in hundreds of dollars a) Find the rate of change. 3 4 ears since used b) Find an function in slope-intercept form where V(t) is value and t is number of ears in use. c) Use this function to find the value at ears. d) What is the domain of this function? 3) What do m and b represent in this function? After a child gets a 'buzz' haircut, the length of his hair L(t) in inches is given b L ( t) = t +, where t is the number of months after the haircut.

8 4) Acme shirt compan uses V ( t) = 000t to determine the salvage value of a color separator t ears after it is put into use. a) What do -000 and 5000 represent? b) How long does it take for the machine to depreciate entirel? c) What is the domain? 4) The function f ( t) = 0.5t + 7 can be used to estimate the cash receipts, in billions of dollars, from farm marketing of cotton t ears after 995. a) What are the cash receipts in 999? b) In what ear was the cash receipts $3.5 billion? 5) In 999, about 48 million Americans used the Internet to find some travel information. B 003, that number had grown to about 64 million Americans. If N(t) represents the number of Americans using the Internet to find some travel information and t represents the number of ears after 999, find the following. a) Write two data points and find a linear function. b) What does the slope of this function represent? c) What does the b value represent?

9 6) Suppose that 6.5 million pounds of coffee are sold when the cost is $8 per pound, and 4.0 million pounds are sold when it is $9 per pound. Let p = the number of pounds of coffee sold (in millions) and C(p) = the cost per pound. a) Write the data points (p, C(p)) and find the average rate of change. b) Find a linear function for this data. c) Use the linear function to predict how man pounds will be sold when the cost is $6 per pound.

(4, 2) (2, 0) Vertical shift two units downward (2, 4) (0, 2) (1, 2) ( 1, 0) Horizontal shrink each x-value is multiplied by 1 2

(4, 2) (2, 0) Vertical shift two units downward (2, 4) (0, 2) (1, 2) ( 1, 0) Horizontal shrink each x-value is multiplied by 1 2 Section. Rational Functions 9. i i i i 9i. i i i. i 7i i i i i. 9 i9 i i. g f. g f. g f, ), ), ), ), ), ), ), ), ), ), ), ) Horizontal shift two units to the right Vertical shift two units downward Vertical