Unit 5 notes

Unit 5 Notebook 2012.notebook December 18, 2012

Uni
Found t 5: Equations of Lines
atio
Geome ns of (and all the basics...)
try

Dec 51:49 PM Dec 52:21 PM

Let's start at the beginning...
Do you know where the 4 QUADRANTS are on a
Do you know where the x axis and y axis are on a coordinate axis system?
coordinate axis system?

Where is the ORIGIN?


What is SLOPE? Slope is how much a line slants
Example:
What letter do we use to represent slope??? m

What is the SLOPE formula???


1


Do you recall what the 4 types of slope look like?
What is the SLOPE INTERCEPT form of a line???


What does m stand for?
What is the slope
m stands for SLOPE. m tells (m) and y intercept
you how to MOVE from one (b) of this line?
point to another.

What does b stand for?

b represents the Y INTERCEPT.
b tells you where to BEGIN
your graph of a line on the
coordinate axes.


Examples: 3. If (k, 3) is on the line 2y = 9 x, what is the
value of k?
1. Find the slope of the line formed by A(9, 3)
and B(4, 5).
4. What type of slope does the line y = 11
have?
2. Write the equation of the line 5y 10x = 15
in slope intercept form. What is the slope and 5. Write the equation of the line 2y + 8 = x in
y intercept?
slope intercept form. What is the slope and
y intercept?


2


Answers to Homework:  p. 1 2 odds, p. 3 #1 8

1.  B 3.  C 5.  B 7.  C 9.  D

Homework: 11.  C 13.  C 15.  3/5

p. 3
p. 1 2 odds 1.  y = 3/2x + 8 2.  y = 13/11x + 12/11

p. 3 #1 8 3.  y = 9/7x + 1 4.  y = 1/3x 2

5.  y = 6/5x 3 6.  y = 4x 1

7.  y = 11/4x 8 8.  y = 11/8x + 6


Graphing Lines


Homework:
p. 5 & 6 evens


3


al l...
Writing Rec FORMULAS:
Equations of Slope:

Lines Standard Form of a line:  Ax + By = C

Slope Intercept Form of a line:   y = mx + b
(m = slope, b = y intercept)

Point Slope Form of a Line:  y – y1 = m(x – x1)


While y y1 = m(x x1) may be a new formula to
some of you, it is actually just the slope formula
after you cross multiply! How do you write the equation of the line if you are given
a slope and a y- intercept?
Plug directly into the point slope formula for m and b

And if you really do not want to memorize yet Examples:  Write the equation of the line give m and b.
another formula, simply stick to your old
1.  m = 2, b = 5
methods of writing equations of lines!

2.  m = 1/2, b = 7

3.  m = 1, b = 9.2


How do you write the equation of the line if you are given How do you write the equation of the line if you are given
a slope and a point? 2 points?
Find the y- intercept, & then Find the slope.
plug directly into the point slope formula for m and b Use 1 point and your m to find the y- intercept, &
then plug directly into the point slope formula for m and b
Examples:  Write the equation of the line give the point
and the slope.
Examples:  Write the equation of the line give 2 points.
1.  slope = 2, point A(4, 6)
1.  E(3, 2) and F(5, 0)

2.  slope = 1/3, point B(3, 9)
2.  R(5, 1) and T(6, 2)


4


More Practice...

I:  Write each equation in y = mx + b form.
1.  y + 2x = 9 2.  3y 9 = 2x 3.  4y 8x = 12
Homework:
II:  Write the equation of the line in y = mx + b form with the given information.
1.  slope = 9, y intercept = 13 p. 12 #7, 8,
2.  slope = 1/2, passes through the point E(4, 3) 15 18
3.  passes through the points P(7, 6) and Q(8, 3)


p. 12 #7 18 Solutions: Writing Equations of
7.  y = 3/5x + 5 8.  y = 9x + 4 Parallel and
15.  y = x + 2 16.   y = 1/7x + 26/7 Perpendicular Lines
17.  y = x 1 18.  y = 5x  +4


Did you ever stop to really think
I'm sure you know something about why it's important that
about parallel and we have parallel lines?
perpendicular lines...let's
watch this video and check it How can you PROVE that 2
out... lines are parallel???

http://www.youtube.com/watch?v=Gbz7EEiWnv0


5


Parallel lines have the SAME slopes. This Examples I:
Find the slope of a line that is parallel to the given line.
means that the lines MOVE in the same way.
1.  y = 9x 3 2.  y 2x = 3 3.  6x 2y = 8
If you take the red point and
y
10 MOVE it 3 units up and 4 units to
9
8 the right, where will the new Examples II:
7
6 point be??? Now do the same Write an equation of the line that is parallel to y = 7x + 2 with the given y intercept.
5
4 thing with the green point.
3
1.  b = 1 2.  b = 9 3.  b = 0
2
1 x

10 8 6 4 2 0 2 4 6 8 10 Connect the red points and then
2
3 connect the green points. Examples III:
4 Write an equation that is parallel to the given line.
5
6
7 Check to see that the red line 1.  2y = 6x 4 2.  y 1 = x 3. 3x = y 7
8
9
and the green line have the same
10 slopes.


Perpendicular lines are lines that intersect
What types of lines do you see in
and form a right angle. Since these types of
these images?
lines do intersect, they clearly are not
Do these lines have the same parallel, and therefore do not have the same
slope??? slope. Because perpendicular lines meet and
form a right angle, they have a very special
What kinds of slope do these relationship regarding slope. Perpendicular
types of lines have??? lines have negative reciprocal slope.

Example: m=7 m =

m= m = 2

m= m =


Examples:
See if you can fill in the chart below using your 1. Write the equation of the line that is perpendicular to
knowledge of parallel and perpendicular lines. y = 3x 5 and has the same yintercept as y + 2 = 5x.
Slope Parallel Slope Perpendicular Slope

3

4

1/2 2. Write an equation of the line that is perpendicular to
y 4x = 8 and passes through (0, 2).

3. Write an equation of the line that is parallel to
y 3 = 2x and passes through (6, 6).


6


Answers to p. 7 #16 24

16.  C 17.  D
Homework:
18.  C 19.  B

20.  B 21.  B
p. 7 8 #16 24
22.  2/5 23.  y 6 = 3(x 1)
or  y = 3x + 3

24.  A


Group Work!!! Solutions to Worksheet (review for Quiz #8)

Get a partner (or 2) and complete the following 1.  C 2.  A 3.  B
worksheet on writing equations of lines.
4.  2 5.  3/7 6.  4
I will check this and go over this tomorrow!
7.  C 8.  A 9.  D
Good luck. 10.  D 11.  D 12.  D

Quiz #8 tomorrow!!! 13.  y = 2x 1 14.  y = 1/2x 15.

Dec 177:48 AM Dec 177:48 AM

Quiz #8 today!!!
Solving Systems of Equations
by Graphing
No CR due to the Holiday
Break coming up.

Tomorrow we will take the
Unit 5 Pre Test

Dec 177:48 AM Dec 53:50 PM

7


A system of equations is a set or collection of 2 or Systems of equations can be given to you in a
more equations with a set of unknown variables. narrative as shown in the example below:

In solving a system of equations. we try to find The price of a movie matinee ticket is $1.50 for kids and $4
values for each of the unknown variables that will for adults. If the theater took in $124 in ticket sales and 51
satisfy every equation in the system. people attended the matinee, how many were adults and
how many were children?

Or a system of equation can be given algebraically,
We can solve a system of equation using 4 as shown below:
methods:

1. Graphically
2. Algebraically (Elimination)
3. Algebraically (Substitution)
4. Matrices
Today we are going to solve systems by graphing them!!!


Graph these now please!!!



8


So basically, when you are
Remember our friends from WSHS???
asked to find the solutıon They did the "Quad Solve" rap? They have
to a system of equations, another good one for Systems of
you simply fınd the poınt Equations...Let's watch!!!
http://www.youtube.com/watch?v=1qHTmxlaZWQ
of ıntersectıon of the two
lines!!!

Now what....


#1: Let's try this example...Can someone please do it
on the board for me??? PLEASE..........
#2: Let's try this example...Can someone please do it
on the board for me??? PLEASE..........

Solve the following system of equations Solve the following system of equations
GRAPHICALLY: GRAPHICALLY:
y y
5 5

4 4

3 3

2 2

1 1
x x

5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5
1 1

2 2

3 3

4 4

5 5


Can you check your solution set to question #2?

Homework:
p. 13 #1 4


9


Solutions to p. 13 #1 4 Solving Systems of
Equations by
1.  x = 3, y = 2
Elimination
2.  x = 1, y = 1

3.  x = 4, y = 3

4.  x = 2, y = 1


The Elimination Method used to be called the "Addition/ Solve the following system of equations and check:
Elimination Method."  When you solve a system of equations
using the Elimination Method, you will try to get rid of one 4x + 8y = 20
variable by adding the system together.   4x + 2y = 30

Steps:
1.  Make sure the system is set up for elimination (all variables
will align, as will the = sign)
2.  Use simple multiplication to ensure that you can eliminate one
of the variables by addition.  (Sometimes you can skip this step)
3.  Solve the remaining linear equation.
4.  Substitute your answer back into one of the equations and
solve for the other variable.
5.  Check your solution.


Solve the following system of equations and check: Solve the following system of equations:
Try the " Try the "
Cross" Criss Cross" Criss
4x + 9y = 9 method 3x + 7y = 16 method

x 3y = 6 9x + 5y = 16


10


Solutions to p. 15

Homework:   3.  x = 10, y = 1

p. 15 #3, 5, 7, 9 5.  x = 1, y = 3

7.  x = 5, y = 6

9.  x = 1, y = 4


Solving Systems of
The method of solving "by substitution"
Equations by works by solving one of the equations (you
Substitution choose which one) for one of the variables
(you choose which one), and then plugging
this back into the other equation.

***Most of the time, your system will already have one
equation solved for (one of the variables).



11


Solutions to p. 17 #5 8

Homework: 5.  x = 3, y = 2

p. 17 #5 8 6.  x = 2, y = 3

7.  x = 3. y = 6

8.  x = 3, y = 4


Answers to Review Sheet to Unit 5 Post Assessment:

1.  k = 4 2.  y = 7 3.  m = 1

Review for Unit 5 Post 4.  D 5.  B 6.  A
Assessment
7.  y = x + 1 8.  y = 4x 1 9.  y = 2x 1
Get into groups of 4 and
work on the review sheet.
10.  b = 0 11.  m = 2/5 12.  k = 8
Answers will be on the smart
board. Check the answers as 13.  y = 3x + 3 14.  D 15.  A
you go along.

Good luck :) 16.  Graph 17.  x = 2, y = 3 (Quad IV)   18.  x = 4, y = 2

19.  x = 1, y = 2 20.  x = 2, y = 2

Dec 183:19 PM Dec 183:19 PM

Trig Ratios???
Trigonometry Finding Missing Sides


12


Trigonometry Finding the Missing Angle


Trigonometry Word Problems


y = mx + b
Slope formula
Is a poitn on a line?
What is the slope and y intercept?
get y by itself


13




14

Unit 5 notes

Recommended

Recommended

More Related Content

Similar to Unit 5 notes

Similar to Unit 5 notes (6)

More from elk727

More from elk727 (10)

Unit 5 notes