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 y y

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. 1st way to find slope

vertical change rise difference of y's y  y y  y slope = m =    2 1 or 1 2 2nd way horizontal change run difference of x's x2  x1 x1  x2 SLOPE FORMULA: to find y  y slope m  2 1 x2  x1 The vertical change (rise) can be compared to the horizontal change (run) by ‘counting’ on a graph. rd Find the slope of each line described. 3 way to find slope

(4,0) (-1,-1) x

2) 4x  5y  20

3) points: (-2, -8) and (-3, 1)

2 1 4) x  y  1 3 4

5) points: (3, 0) and (-4, -10)

(-2,2)

x (1,-2)

y 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 f (x)  mx  b is slope-intercept form of a linear function. 3  2  7) Write a linear function for a line with slope and y-intercept 0,  . 2  3 

8) Find the slope and y-intercept. 3x  2y  12

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. 5 9) Use the slope and y-intercept to graph the line. f (x)  x  2 2

y 5 10) g(x)   x  3 3

y 11) Determine the slope and y-intercept, then graph. 4x  2y  8

12) Graph h(x)  2 APPLICATIONS 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.

r 24 r a l e l t o u d p

f 18 m o o s c

d f e o r

d e n u 12 l u a h v n i 6

1 2 3 4 years since 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? 3) What do m and b represent in this function? After a child gets a 'buzz' haircut, the length 1 of his hair L(t) in inches is given by L(t)  t 1, where t is the number of months after the 2 haircut.

4) Acme shirt company uses V (t)  2000t 15000 to 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 f (t)  0.5t  7 can 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 billion?