Download - Entry Task 11/21/2011
Entry Task 11/21/2011Simplify 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.
3259
CF
Chapter 4
A1.2.B on wallA1.3.A on wallA1.3.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 linesA1.4.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 representA1.4.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.
Algebra 1
Section 4.1Objective: 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 pairIn (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 pairY-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 PointsPlot 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 plotTitle- have oneAxis- label themIntervals- make sure all numbers are included and you use enough of the graph
Labels- units includedScale-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?
A B
C
DE
Entry Task 12/4/20121.) Write the ordered pair that
goes with each of the points graphed below and tell what quadrant it is in.
2. Solve: 3x+7 = 19
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 below.3.) Is this a scatter plot?4.) What might we title it?5.) What can we say about how a husband’s age changes as a wife’s age changes?
Entry Quiz 11/19/2010Graph 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 WorkPg. 214 #1-10
Entry Task 11/22/2010Graph the following equation using a table
20515 yx
Is the point (3,-4) a solution to this equation? Why?
Class WorkPg. 214-215 #12-14, 36, 41, 45, 48,50, 52-55, 60
EC pg. 216-217 #67-75
Entry Task 11/29/2010Grab an entry task sheet from the front of
the room then Graph the following equation using a table
73 xy
Is the point (3,-4) a solution to this equation? Why?
Section 4.3Objective: Find the intercepts of the graph
of a linear equation. Use the intercepts to make a quick graph of the linear equation.
VocabularyX-intercept- the
point at which the graph crosses the x-axis.
Y-intercept-the point at which the graph crosses the y axis
http://en.labs.wikimedia.org/wiki/Algebra/Function_Graphing
Finding interceptsFind the x and y –intercepts for
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
632 yx
Using interceptsUse the x and y-intercepts found previously
to graph 632 yx
Homework
pg. 221 #1-9
Entry Task 11/30/2010Find the x-and y-intercepts of the equation
Graph the Equation using the x-and y-intercepts
1234 yx
HomeworkPg. 221 #10-19, 26-28
EC pg. 222 #56-66
Entry Task 12/01/2010Find the x-and y-intercepts of the equation
Graph the Equation using the x-and y-intercepts
yx 42
Section 4.4Objective: Find the slope of a line using two
of its points
SlopeThe 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.
http://intermath.coe.uga.edu/dictnary/descript.asp?termID=336
313
slope
12
12
____
xxyy
xinchangeyinchange
runriseslope
Finding slope from two pointsPoint 1 (x1, y1)Point 2 (x2, y2)
Point 1 (2, 1)Point 2 (3, 5)
12
12
____
xxyy
xinchangeyinchange
runriseslope
Positive or negative slopeA line has positive slope if it rises from left to right
A line has negative slope if it falls from left to right
A line has a slope of zero if it is a horizontal line
A line has an undefined slope if it is a vertical line
0m 0m 0m m is undefined
Parallel and Perpendicular linesParallel 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
HomeworkPg. 230 #5-10, 12-13, 35-37
E.C. pg. 230 #20-30
Entry Task 12/02/2010Find the slope of the line containing the points
(3, -1) and (4, -2)
Is the slope positive, negative, zero, or undefined?
Section 4.4Objective: Interpret the slope as a rate of
change in real-life situations.
Slope as a rate of changeRate of change- compares two different
quantities that are changing.
HomeworkPg. 231 #51-61E.C. pg. 230 #47-50, 62-65
Entry Task 12/03/2010The 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 DayWork on worksheet
Entry Task 12/07/2010Find 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 4.5Objective: Write linear equations that
represent direct variation. Use a ratio to write an equation for direct variation.
Direct VariationTwo 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 variationTwo quantities that vary directly are said to
have direct variation.A direct variation is a linear function where
the y-intercept is zero.
Example :Find the constant of variation and the slope
of each direct variation model
Work on problems 1-8 and 12-16even
xy 2 xy21
(1, 2)(0, 0) (0, 0)
(2, -1)
ExampleThe 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
HomeworkPg.237 #1-8, 12-16even, 23-25
E.C. pg. 238 #26-29, 34-37
No entry taskIf 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 12/09/2010Let 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 4.6Objective: 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 downThe 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 + 3The slope is 2The y-intercept is (0,3)
1Two 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 variationTwo 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-interceptGraph 3x + y = 2Step 1: write in slope-intercept formStep 2: find the slope and y-interceptStep 3: Plot the point (0,b)Step 4: Draw a slope triangle to locate a second point.
runrisem
Parallel linesTwo 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
HomeworkPg. 244 #28-39E.C. pg. 245 #56-65
Entry Task 12/10/2010Graph the following line using slope and y-
intercept
Write an equation for a line parallel to this one.
151
xy
Agenda for todayWork on the quiz
When you finish work on pg. 244 #13-49 every third problem due Monday
Entry Task 12/13/2010Graph 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 4.8Objective: Identify when a relation is a
function. Write equations in function form and evaluate functions.
Identifying functionsA 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.
1234
Input Output
24
5
Input Output1234
57
9
Vertical line test
Do problems 7, 8, 9
Function notationf(x) is read “f of x” or “the value of f at x”.
It Does not mean f times xf(x) is called function notation.
Write y = 3x + 2 in function notation
Evaluating a functionEvaluate the functions when x = -2
32)( xxf xxg 5)(
HomeworkPg. 259 #11-19, 20-22,32-34
Entry Task 12/15/2010Evaluate the following functions for x = 2, x
= 0, and x = 3110)( xxf 63)( xxh