Lesson 12 Section 2.3
Lesson 12 Section 2.3
Compare the graphs of the lines below.
A B C
y = 2xy = 2x + 3y = 2x - 4
xyxyxy
00030-4
-1-2-11-1-6
242720
-3-6-3-3-310
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 =
SLOPE FORMULA:
The vertical change (rise) can be compared to the horizontal change (run) by ‘counting’ on a graph.
Find the slope of each line described.
1)
2)
3)points: (-2, -8) and (-3, 1)
4)
5)points: (3, 0) and (-4, -10)
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 is slope-intercept form of a linear function.
7)Write a linear function for a line with slope and y-intercept .
8)Find the slope and y-intercept.
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.
10)
11)Determine the slope and y-intercept, then graph.
12)Graph
APPLICATIONS
1)Year% of U.S. homes with multiple computers
199710
199813.6
199917.2
200020.8
200124.4
Notice: Each year, the percent of U.S. homes with multiple computers grew by 3.6%. This is called the rate of changeand 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?
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 by , where t is the number of months after the haircut.
4)Acme shirt company uses 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 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?