1 / 58

# Entry Task 11/21/2011 - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

• 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

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?

• 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

• 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

• Pg. 214 #1-10

• Graph the following equation using a table

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

• 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

• 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 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

• 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

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

### Homework

• pg. 221 #1-9

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

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

### Homework

• Pg. 221 #10-19, 26-28

• EC pg. 222 #56-66

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

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

### Section 4.4

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

### 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

• Point 1 (x1, y1)

• Point 2 (x2, y2)

• Point 1 (2, 1)

• Point 2 (3, 5)

### 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 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

• 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

• 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

• 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 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

(1, 2)

(0, 0)

(0, 0)

(2, -1)

### 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

• 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

• 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:

• 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

• 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

• 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

### Homework

• Pg. 244 #28-39

• E.C. pg. 245 #56-65

• Graph the following line using slope and y-intercept

• 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

• 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

Output

2

4

5

InputOutput

1

2

3

4

1

2

3

4

5

7

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

### Homework

• Pg. 259 #11-19, 20-22,32-34