Download Chapter 4 Power Point

Entry Task 11/21/2011
 Simplify completely.
1.) 2v(4v2 – 3) + 3(5v3 + 2v)
2.) 3x – 4x(x-5) + (2x-7)(3x)
3.) 4b4 – 3b(2b2 + 3b) + 3b2(b2 + 2b) -4b2
4.) make an input-output table for the following function
when the domain is -5, 0, 5, 10 degrees Celsius.
9
F  C  32
5
Algebra 1
Chapter 4
A1.2.B on wall
A1.3.A on wall
A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words,
and make connections among these representations.
A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations
for parallel and perpendicular lines
A1.4.E Describe how changes in the parameters of linear functions and functions containing an
absolute value of a linear expression affect their graphs and the relationships they represent
A1.4.B Write and graph an equation for a line given the slope and y-intercept, the slope and a
point on the line, or two points on the line and translate between forms of linear equations.
Section 4.1
 Objective: Plot points in a coordinate plane.
http://www.rblewis.net/technology/EDU506/WebQuests/co_plane/coplane.html
Entry Task; copy this down in your math notebooks, if you
finish, do it again.
 Coordinate Plane- two real number
lines that intersect at a right angle.
 Ordered Pair- the written
representation of a point on the
coordinate plane
(2,1)
 X-coordinate- the first number in an ordered pair
 Y-coordinate-the second number in an ordered pair
In (2,1), 2 is the X-coordinate and 1 is the Y coordinate
 Graph- the point in the plane that corresponds to an
ordered pair.
Vocabulary cont.
 X-coordinate- the first number in an ordered pair
 Y-coordinate-the second number in an ordered pair
 In (2,1), 2 is the X-coordinate and 1 is the Y coordinate
 Graph- the point in the plane that corresponds to an ordered
pair.
Plotting Points
 Plot the following
points
 (3,4)
 (-2,-3)
 (2,0)
Section 4.1 cont.
 Objective: Draw a scatter plot and make predictions about
real-life situations
http://onlinestatbook.com/chapter4/graphics/age_scatterplot.gif
Making a scatter plot
 Title- have one
 Axis- label them
 Intervals- make sure all numbers are
included and you use enough of the
graph
 Labels- units included
 Scale-use at least 50% of the graph
Making a scatter plot cont.
 A scatter plot is a graph that compares two quantities. When
we make a scatter plot we do not connect the dots.
Look at the graph to the right.
Is this a scatter plot?
What might we title it?
What can we say about how a
husband’s age changes as a
wife’s age changes?
Entry Task 12/4/2012
 1.) Write the ordered pair that goes with
 A scatter plot is a graph that compares
two quantities. When we make a scatter
plot we do not connect the dots.
each of the points graphed below and tell
what quadrant it is in.
Look at the graph below.
3.) Is this a scatter plot?
4.) What might we title it?
A
5.) What can we say about how a
B
husband’s age changes as a wife’s age
changes?
C
E
D
 2. Solve: 3x+7 = 19
Entry Quiz 11/19/2010
 Graph the following points on the graph paper provided:
 A(3,-2) B(2,-5) C(-3,-4) D(4,1) E(0,-4)
 On the back, solve the following and show your work:
1.) 4x-5= 20
2.) 2(3x+1)-4x=-x – 3
3.) Use the scatter plot to the right to
determine how the mean annual
temperature in Nevada changes as the
elevation increases.
Class Work
Pg. 214 #1-10
Entry Task 11/22/2010
 Graph the following equation using a table
15 x  5 y  20
Is the point (3,-4) a solution to this equation?
Why?
Class Work
Pg. 214-215 #12-14, 36, 41, 45,
48,50, 52-55, 60
EC pg. 216-217 #67-75
Entry Task 11/29/2010
 Grab an entry task sheet from the front of the room then
 Graph the following equation using a table
y  3x  7
Is the point (3,-4) a solution to this equation?
Why?
Section 4.3
 Objective: Find the intercepts of the graph of a linear
equation. Use the intercepts to make a quick graph of the
linear equation.
Vocabulary
 X-intercept- the
point at which the
graph crosses the xaxis.
 Y-intercept-the point
at which the graph
crosses the y axis
http://en.labs.wikimedia.org/wiki/Algebra/Function_Graphing
Finding intercepts
 Find the x and y –intercepts for
2x  3y  6
 To find the x intercept plug 0 in for y and solve for x
 To find the y intercept plug 0 in for x and solve for y
Using intercepts
 Use the x and y-intercepts found previously to graph
2x  3y  6
Homework
pg. 221 #1-9
Entry Task 11/30/2010
 Find the x-and y-intercepts of the equation
4 x  3 y  12
 Graph the Equation using the x-and y-intercepts
Homework
Pg. 221 #10-19, 26-28
EC pg. 222 #56-66
Entry Task 12/01/2010
 Find the x-and y-intercepts of the equation
x  2  4y
 Graph the Equation using the x-and y-intercepts
Section 4.4
 Objective: Find the slope of a line using two of its points
3
slope   3
1
Slope
 The slope of a
nonvertical line is
the number of units
the line rises or falls
for each unit of
horizontal change
from left to right.
rise change _ in _ y y2  y1
slope 


run change _ in _ x x2  x1
http://intermath.coe.uga.edu/dictnary/descript.asp?termID=336
Finding slope from two points
 Point 1 (x1, y1)
 Point 2 (x2, y2)
rise change _ in _ y y2  y1
slope 


run change _ in _ x x2  x1
 Point 1 (2, 1)
 Point 2 (3, 5)
Positive or negative slope
A line has
positive slope if
it rises from
left to right
m0
A line has
negative slope
if it falls from
left to right
m0
A line has a slope A line has an
undefined slope
of zero if it is a
horizontal line if it is a vertical
line
m0
m is
undefined
Parallel and Perpendicular lines
 Parallel lines never intersect.
 If two lines are parallel, their slopes are
the same.
 Perpendicular lines intersect at a right
angle.
 If two lines are perpendicular then
their slopes are opposite reciprocals. In
other words you turn it upside down
and change the sign
Homework
Pg. 230 #5-10, 12-13, 35-37
E.C. pg. 230 #20-30
Entry Task 12/02/2010
 Find the slope of the line containing the points (3, -1) and (4, -2)
 Is the slope positive, negative, zero, or undefined?
Section 4.4
 Objective: Interpret the slope as a rate of change in real-life
situations.
Slope as a rate of change
 Rate of change- compares two different quantities that are
changing.
Homework
Pg. 231 #51-61
E.C. pg. 230 #47-50, 62-
65
Entry Task 12/03/2010
 The bottom of Bluewood ski resort is 4545ft, the top is 5670
ft.. If the horizontal distance from the bottom of the lift to
the top of the lift is 2000 ft, what is the average slope of the
chair lift at Bluewood?
Review Day
 Work on worksheet
Entry Task 12/07/2010
 Find the slope of the line containing the points (2, 5) and (6, -5)
 If x is time in seconds and y is distance in feet, what does the
slope represent? What is the unit for the slope?
Section 4.5
 Objective: Write linear equations that represent direct
variation. Use a ratio to write an equation for direct
variation.
Direct Variation
 Two variables x and y are said to vary directly if
there is a nonzero number k such that the following
is true:
 The number k is the constant of variation
 Two quantities that vary directly are said to have
direct variation.
 A direct variation is a linear function where the yintercept is zero.
Example:
 Find the constant of variation and the slope of each direct
variation model
y  2x
(0, 0)
(1, 2)
1
y x
2
(0, 0)
(2, -1)
 Work on problems 1-8 and 12-16even
Example
 The variables x and y vary directly. When x = 5 and y = 20.
 Write an equation that relates x and y.
 Find the value of y when x = 10
 Work on homework problems 23-25
Homework
Pg.237 #1-8, 12-16even, 23-25
E.C. pg. 238 #26-29, 34-37
No entry task
 If you are not finished with the benchmark test find the desk
your test is on and do it.
 If you are finished work quietly on last nights homework or
pg. 237 #9-11, 21, 22, 30-33
E.C. pg. 238 #26-29, 34-37
Entry Task 12/09/2010
 Let x and y vary directly when x = 3 and y =9.
 Find the constant of variation
 Write the equation for the direct variation.
 Graph it and identify the slope.
Section 4.6
 Objective: Graph a linear equation in slope-intercept form.
Graph and interpret equations in slope-intercept form that
model real-life situations.
Entry Task 02/04/2013 copy this down
 The linear equation y = mx + b is written in slope-intercept form.
 The slope is m.
 The y-intercept is the point (0,b).
 Example: y = 2x + 3
 The slope is 2
 The y-intercept is (0,3)
 Two variables x and y are said to vary directly if there is a nonzero
number k such that the following is true:
1
 The number k is the constant of variation
 Two quantities that vary directly are said to have direct variation.
 A direct variation is a linear function where the y-intercept is zero.
Graphing using slope and y-intercept
 Graph 3x + y = 2
 Step 1: write in slope-intercept form
 Step 2: find the slope and y-intercept
 Step 3: Plot the point (0,b)
 Step 4: Draw a slope triangle to
locate a second point.
rise
m
run
Parallel lines
 Two different lines in the same plane are parallel if they do
not intersect.
 How can we tell if to lines are parallel without graphing
them?
The red
lines have
slope m=-1
The blue
lines are
vertical
Homework
Pg. 244 #28-39
E.C. pg. 245 #56-65
Entry Task 12/10/2010
 Graph the following line using slope and y-intercept
1
y   x 1
5
 Write an equation for a line parallel to this one.
Agenda for today
 Work on the quiz
 When you finish work on pg. 244 #13-49 every third
problem due Monday
Entry Task 12/13/2010
 Graph the following situation:
 You start 165 miles from home and drive towards home at 55
miles per hour for 3 hours, where d is your distance from
home.
Section 4.8
 Objective: Identify when a relation is a function. Write
equations in function form and evaluate functions.
Identifying functions
 A relation is any set of ordered pairs.
 A Function is a relation where for every input there is
exactly one output.
 Decide if the following are functions, state the domain and
range if they are.
Input
1
2
3
4
Output
2
4
5
Input Output
1
5
2
7
3
4
9
Vertical line test
Do problems 7, 8, 9
Function notation
 f(x) is read “f of x” or “the value of f at x”. It Does not mean
f times x
 f(x) is called function notation.
 Write y = 3x + 2 in function notation
Evaluating a function
 Evaluate the functions when x = -2
f ( x)  2 x  3
g ( x)  5 x
Homework
Pg. 259 #11-19, 20-
22,32-34
Entry Task 12/15/2010
 Evaluate the following functions for x = 2, x = 0, and x = 3
f ( x)  10 x  1
h( x )  3 x  6