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