Entry task 11 21 2011
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Entry Task 11/21/2011. Simplify completely. 1.) 2v(4v 2 – 3) + 3(5v 3 + 2v) 2.) 3x – 4x(x-5) + (2x-7)(3x) 3.) 4b 4 – 3b(2b 2 + 3b) + 3b 2 (b 2 + 2b) -4b 2 4.) make an input-output table for the following function when the domain is -5, 0, 5, 10 degrees Celsius. Algebra 1.

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Entry Task 11/21/2011

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Entry task 11 21 2011

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.


Algebra 1

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

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

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

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

Plotting Points

  • Plot the following points

  • (3,4)

  • (-2,-3)

  • (2,0)


Section 4 1 cont

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

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

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

Entry Task 12/4/2012

  • A scatter plot is a graph that compares two quantities. When we make a scatter plot we do not connect the dots.

  • 1.) 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

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?

A

B

C

E

D


Entry quiz 11 19 2010

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= 202.) 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

Class Work

  • Pg. 214 #1-10


Entry task 11 22 2010

Entry Task 11/22/2010

  • Graph the following equation using a table

Is the point (3,-4) a solution to this equation? Why?


Class work1

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

Entry Task 11/29/2010

  • Grab an entry task sheet from the front of the room then

  • Graph the following equation using a table

Is the point (3,-4) a solution to this equation? Why?


Section 4 3

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

Vocabulary

  • X-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 intercepts

Finding intercepts

  • Find 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


Using intercepts

Using intercepts

  • Use the x and y-intercepts found previously to graph


Homework

Homework

  • pg. 221 #1-9


Entry task 11 30 2010

Entry Task 11/30/2010

  • Find the x-and y-intercepts of the equation

  • Graph the Equation using the x-and y-intercepts


Homework1

Homework

  • Pg. 221 #10-19, 26-28

  • EC pg. 222 #56-66


Entry task 12 01 2010

Entry Task 12/01/2010

  • Find the x-and y-intercepts of the equation

  • Graph the Equation using the x-and y-intercepts


Section 4 4

Section 4.4

  • Objective: Find the slope of a line using two of its points


Slope

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.

http://intermath.coe.uga.edu/dictnary/descript.asp?termID=336


Finding slope from two points

Finding slope from two points

  • Point 1 (x1, y1)

  • Point 2 (x2, y2)

  • Point 1 (2, 1)

  • Point 2 (3, 5)


Positive or negative slope

Positive or negative slope

A line has negative slope if it falls from left to right

A line has an undefined slope if it is a vertical line

A line has positive slope if it rises from left to right

A line has a slope of zero if it is a horizontal line

m is undefined


Parallel and perpendicular lines

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


Homework2

Homework

  • Pg. 230 #5-10, 12-13, 35-37

  • E.C. pg. 230 #20-30


Entry task 12 02 2010

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 41

Section 4.4

  • Objective: Interpret the slope as a rate of change in real-life situations.


Slope as a rate of change

Slope as a rate of change

  • Rate of change- compares two different quantities that are changing.


Homework3

Homework

  • Pg. 231 #51-61

  • E.C. pg. 230 #47-50, 62-65


Entry task 12 03 2010

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

Review Day

  • Work on worksheet


Entry task 12 07 2010

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

Section 4.5

  • Objective: Write linear equations that represent direct variation. Use a ratio to write an equation for direct variation.


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 y-intercept is zero.


Example

Example:

  • Find the constant of variation and the slope of each direct variation model

  • Work on problems 1-8 and 12-16even

(1, 2)

(0, 0)

(0, 0)

(2, -1)


Example1

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


Homework4

Homework

  • Pg.237 #1-8, 12-16even, 23-25

  • E.C. pg. 238 #26-29, 34-37


No entry task

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

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

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.


E ntry task 02 04 2013 copy this down

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:

  • 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.

1


Graphing using slope and y intercept

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.


Parallel lines

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 blue lines are vertical

The red lines have slope m=-1


Homework5

Homework

  • Pg. 244 #28-39

  • E.C. pg. 245 #56-65


Entry task 12 10 2010

Entry Task 12/10/2010

  • Graph the following line using slope and y-intercept

  • Write an equation for a line parallel to this one.


Agenda for today

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

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

Section 4.8

  • Objective: Identify when a relation is a function. Write equations in function form and evaluate functions.


Identifying 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

Output

2

4

5

InputOutput

1

2

3

4

1

2

3

4

5

7

9


Vertical line test

Vertical line test

Do problems 7, 8, 9


Function notation

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

Evaluating a function

  • Evaluate the functions when x = -2


Homework6

Homework

  • Pg. 259 #11-19, 20-22,32-34


Entry task 12 15 2010

Entry Task 12/15/2010

  • Evaluate the following functions for x = 2, x = 0, and x = 3


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