Lesson 12 Section 2.3 Compare the graphs of the lines below. A B C y = 2x y = 2x + 3 y = 2x - 4 x y x y x y 0 0 0 3 0 -4 -1 -2 -1 1 -1 -6 2 4 2 7 2 0 -3 -6 -3 -3 -3 10 How does each point of graph B compare with graph A (directly below)? How does each point of graph C compare with graph A (directly above)? If the equations of B and C are considered to be in the form y = mx + b, the point (0, b) represents the y-intercept. The value of m represents the 'slant' of the line, called the slope. slope = m = 21211212or s x'of differencesy' of difference runrise change horizontalchange verticalxxyyxxyy−−−−=== SLOPE FORMULA: 1212xxyym−−= y x y 1st way to find slope 2nd way to find slopeThe vertical change (rise) can be compared to the horizontal change (run) by ‘counting’ on a graph. Find the slope of each line described. 2) 2054=−yx 3) points: (-2, -8) and (-3, 1) 4) 14132=− yx 5) points: (3, 0) and (-4, -10) x y (-1,-1) (4,0) x y (-2,2) (1,-2) 3rd way to find slope 1) 6)Slope-Intercept Form: The form y = mx + b is called the slope-intercept form where m is the slope and (0, b) is the y-intercept. The form bmxxf+=)( is slope-intercept form of a linear function. 7) Write a linear function for a line with slope 23and y-intercept −32,0. 8) Find the slope and y-intercept. 1223=−yx You can graph a line using the slope and y-intercept. • Begin on the y-axis at the y-intercept. • Count ‘up or down’ corresponding to rise, then ‘left or right’ corresponding to run to find another point. • Draw the line. 9) Use the slope and y-intercept to graph the line. 225)(−= xxf x y10) 335)(+−= xxg 11) Determine the slope and y-intercept, then graph. 824=−yx x y x y12) Graph 2)(−=xhAPPLICATIONS 1) Year % of U.S. homes with multiple computers 1997 10 1998 13.6 1999 17.2 2000 20.8 2001 24.4 Notice: Each year, the percent of U.S. homes with multiple computers grew by 3.6%. This is called the rate of change and is equal to the slope, if a graph was made with the x-axis representing years and y-axis representing percent. 2) The graph below represent the value of a computer model (in hundreds of dollars) for a number of years after it is used. a) Find the rate of change. b) Find an function in slope-intercept form where V(t) is value and t is number of years in use. c) Use this function to find the value at 2 years. d) What is the domain of this function? value of computer in hundreds of dollars 30 24 18 12 6 0 1 2 3 4 years since used3) 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 by 121)(+= ttL, where t is the number of months after the haircut. 4) Acme shirt company uses 150002000)(+−=ttVto determine the salvage value of a color separator t years after it is put into use. a) What do -2000 and 15000 represent? b) How long does it take for the machine to depreciate entirely? c) What is the domain? 4) The function 75.0)(+−=ttfcan be used to estimate the cash receipts, in billions of dollars, from farm marketing of cotton t years after 1995. a) What are the cash receipts in 1999? b) In what year was the cash receipts $3.5
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