geometricgeometric advanced alg/trig chapter 11 – sequences and series sequences (an ordered list...
TRANSCRIPT
Geometric
ADVANCED ALG/TRIG
Chapter 11 – Sequences and Series
Sequences(an ordered list of
numbers)
GeometricR = common
ratioGeometric mean = square root of
product of 2 numbers
Recursive formula
an = an-1 r; a1
given
Explicit formulaan = a1 r(n-1)
ArithmeticD = common
differenceArithmetic mean
= sum of 2 numbers divided
by 2 (the average)
Recursive formula
an = an-1 + d; a1
given
Explicit formulaan = a1 + (n-1)d
Series(sum of terms in a
sequence)
GeometricFINITE – ends; has a sum
INFINITEConverges when |r|
<1; approaches a limitDiverges when |r|> 1; does not approach a
limit
Sum of a Finite
Geometric Series
Sn = a1(1-rn) 1 - r
Sum of an Infinite Geometric Series
Sn = a1
1 - r
ArithmeticFinite – endsInfinite – does not end…Summation Notationuses Sigma ; has lower and upper limits
Sum of a Finite Arithmetic Series
S = n/2(a1 + an)
Conclusion about these features
Cubes are Three Dimensional
FeaturesMain ideas Features
Cube Square
Conclusion about these features
Squares areOne Dimensional
Count the sidesA cube has ______ sides.
Count the sidesA square has______ sides.
Sides
Conclusion about this main idea
The sides are shaped like
squares
Hold the block and count the cornersA cube has _______ corners.
Touch each corner with your pencilA square has______ corners.
Corners
Conclusion about this main idea
A cube has more corners
Build something
Make a design on paper
What can you do with
it?
Conclusion about this main idea
A square is easier to draw and use
Divide
Divide both numbers and start again
3 3-3 =1 6 6-3 =2
Is there a number that will divide into both numbers?No, the fraction is reduced 4 7Yes, keep going
Is the numerator 1 less than the denominator?Yes, the fraction is reduced 5/6
No, keep going 5/3 = 1 2/3
Is the numerator a “1”?
Yes, the fraction is reduced 1/6
No, keep going 2/4 = 1/2
How to tell if a fraction is reduced to lowest terms
Reducing Fractions Is about …
1. Identify the slope (m) and the y-intercept (b).Example: m = 2, b = -1
3. Use the slope the locate a second point.
4. Draw a line through the two points.
2. Graph the y-intercept on the y-axis. Example:
2. Find the y-intercept. Let x=0 and solve the equation for y.Example: 3(0) – 2y = 6 -2y = 6 y=-3
1. Find the x-intercept. Let y=0 and solve the equation for x.Example: 3x – 2(0) = 6 3x = 6 x=2
Slope-intercept form: y = mx + b
Example: y= 2x - 1
Standard Form:Ax + By = C
Example: 3x – 2y = 6
4. Draw a line through the two points.
3. Graph the x-intercept on the x-axis and the y-intercept on the y-axis.
Graphing Linear Equations
Key Topic
is about... Angles
4 kinds of angles
Straight Acute
Right Obtuse
180 0 180
does not bend
less than 90 0
1 -- 89 0 0
small angle
always 90 0
square corners
perpendicular
greater than 90 0
0 91 - 179 0
wide angle angle larger than right angle
type of angle is determined by the degree of arch
© 2001 Edwin S. Ellis
So what? What is important to understand about this?
SYSTEMS OF LINEAR INEQUALITIES
First Inequalit
y
1 Graph: a.Solve for y and identify the
slope and y-intercept. b.Graph the y-intercept on the
y-axis and use the slope to locate another point.
-or- find the x and y intercepts and graph them on the x and y axis.)
2 Determine if the line is solid or dashed.
3 Pick a test point and test it in the original inequality.
• If true, shade where the point is.
• If false, shade on the opposite side of the line.)
Second Inequalit
y
1 Graph: a.Solve for y and identify the
slope and y-intercept. b.Graph the y-intercept on the
y-axis and use the slope to locate another point.
-or- find the x and y intercepts
and graph them on the x and y axis.)
2 Determine if the line is solid or dashed.
3 Pick a test point and test it in the original inequality.
• If true, shade where the point is.
• If false, shade on the opposite side of the line.)
Solution
1 Darken the area where the shaded regions overlap.
2 If the regions do not overlap, there is no solution.
Check
1 Choose a point in the darkened area.
2. Test in both original inequalities.
3. Correct if both test true.
Copyright 2005 Edwin Ellis
Key Topic
is about... POLYGONS
labeling shapes according to the number of sides
Triangle Quadrilateral Pentagon Hexagon
Octagon Decagon
3 sides
3 angles
4 sides
4 angles
5 sides
5 angles
6 sides
6 angles
8 sides
8 angles
10 sides
10 angles
TRI means 3 QUAD means 4 Pent means 5 Hex means 6
Oct means 8 Dec means 10
Polygon is a closed, flat figure with straight lines for sides
© 1998 Edwin S. Ellis
So what? What is important to understand about this?
These are the steps to …Ratio Method Factor Ax2 + Bx + C
Five StepsCopyright 2003 Edwin Elliswww.GraphicOrganizers.com
Write the first ratio in the first binomial and the second ratio in the second binomial. 8(3x – 1) ( x – 1) Check using FOIL.
Step 5
Write the ratio A/ Factor. Write the ratio Factor / C. Reduce. 3/1 1/1 are reduced.
Step 4
Example: 24m2 – 32m + 8
Factor out the GCF 8(3m2 – 4m + 1)
Write two binomials 8 ( ) ( )Signs: + C signs will be the same sign as the sign of b . - C negative and positive
8( - ) ( - )
Find AC
AC = 3
Find the factors of AC that will add or subtract (depends on the sign of c) to give u B. 3 and 1 are the factors of AC that will add (note c is +) to give B.
Step 1
Step 2
Step 3
Why are these steps important?
Following these steps will allow one to factor any polynomial that is not prime.
Factoring a quadratic trinomial enable one to determine the x-intercepts of the parabola.
Factoring also enables one to use the x-intercepts to graph.
menu
Key Topic is about...
Essential Details
Divisibility
two (2) - if a number ends with 0,2,4,6,8
dividing numbers that don’t have remainders
five (5) - if a number ends with 0 or 5
ten (10) - if a number ends with 0
three (3) - if the sum of the digits can be
nine (9) - if the sum of the digits can be
It’s an easier way to divide BIG numbers!
Lesson by Tuwanna McGee
So what? What is important to understand about this?
divided by 3
divided by 9
Detail Essential because...
Main idea
Detail Essential because...
Main idea
is about... Lines
2 kinds of lines
ParallelPerpendicular
Intersect / meet
form right angles
forms a square corner
never intersect, meet, or touch
same plane
go in same direction
There are only two types of lines
© 1998 Edwin S. Ellis Key Topic
So what? What is important to understand about this?
Word Walls
New WordDefinition Picture
Knowledge Connection
triangle3 sides 3 angles “tri” means 3
Looks like a pyramid
quadrilateral4 sides 4 angles “quad” means 4
Looks like a box
hexagon6 sided box; 6 angles “hex” means 6
Looks like a stop sign
pentagon5 sided box; 5 angle “pent” means 5
Looks like a house
Graphing a Quadratic Function by Hand Is about …
These options allow one to graph any quadratic function. A quadratic function models many of the physical, business, and area problems one see in real world situation. For example: maximize height of a projectile; maximize profit or revenue; minimize cost; Maximize/ minimize area or volume
Main Idea
Details
1Complete the square in x to write the quadratic function in the form f(x) = a(x – h)2 + k.
2Graph the function in stages using transformations.
Option 1
Main Idea
Details
1Determine the vertex ( -b/2a, f(-b/2a)).2Determine the axis of symmetry, x = _b/2a3Determine the y-intercept, f(0).4a) If the discriminant > 0, then the graph of the function has two x-intercepts, which are found by solving the equation.b) If the discriminant = 0, the vertex is the x-intercept.c) If the discriminant < 0, there are no x-intercepts.5Determine an additional point by using the y-intercept the axis of symmetry.6Plot the points and draw the graph.
menu
Option 2
menuCopyright 2003Edwin EllisGraphicorganizers.com
Product propertylog bxy = logbx + logb y
Power propertylog bN x = x logb N
Quotient propertylog bx / logb y = logbx -
logb y
PROP ERTIES
Exponential y = abx
Asymptote = x-axis, y = 0y-intercept (0,1)
For both graphs, relate to parent function and label
intercepts.
Logarithms Logb N = PAsymptote = y-axis, x = 0
x-intercept = (1,0)
GRAP HS
Exponential y = abx
b>1 = growth, 0<b<1 = decay
Common Log = base 10; log
Natural Log = base e; ln
Logarithms Logb N = PB = base, N = #, P =
power
EXPRESSIONS
Exponential y = abx
Take log of both sides.
Use properties whilesolving and simplify.
Logarithms Logb N = PWrite in exponential form.
EQUATIONS
Advanced Alg/Trig Chapter 8
EXPONENTIALS AND LOGARITHMS
Find the vertex and make a table.General form: y = │mx + b│ + c
So what? What is important to
understand about this?
The graph is always a “V”. A minus sign outside the absolute value bars cause the “V” to be flipped upside down. The m value in the equation affects the slope of the sides of the “V”.
1Graph the parent function. Its vertex is usually the origin.
2Translate h units left (if h is positive) or right (if h is negative).3Translate k units up (if k is positive) or down (if k is negative).
Example: y = -│2x - 4│+ 1Parent function: -│2x│
Translate the parent function.Parent function: y = │mx │ Translated form: y = │mx ± h│ ± k
Graphing Absolute Value Equations
1Find the vertex using (-b/m, c). 2Make a table of values.3Choose values for x to the left and to the right of the vertex. Find the corresponding values of y.4Graph the function.
Example: y =│2x - 4│+ 1 Vertex (-(-4)/2 , 1 ) = (2, 1) x y
3 │2(3) - 4│+ 1=│2│+1=3
1 │2(1) - 4│+1=│-2│+1=3
Hot Dog Gist & Details © 2003 Edwin Elliswww.GraphicOrganizers.com
Exponents
Zero Exponents
n0 = 1 -n0 = -1 (-n) 0 = 1
Details
Gist
Multiplying Like Bases
am an = am + n
Details
Gist
Quotient to a Power
(a/b)n = an/ bn
Details
Gist
Dividing Like Bases
am = am-n
an
Details
Gist
Negative Exponents
n-1 = 1/n 1/n-1 = nDetails
Gist
Power to a Power
(am)n = amn
Details
Gist
Product to a Power
(ab)n = an bn
Details
Gist
Details
Gist
PolynomialsAlgebraic expressions of problems when the task is to determine the value of one unknown number… X
So what? What is important to understand about this?
The concept is important for the AHSGE Objective I-2. You may add or subtract polynomials when determining or representing a customer’s order at a store.
Main idea
Monomials
Example:4x3 Cubic 5 Constant
Number of terms:One = “mon”4x3
Degree:Sum the exponents of its variables
Main idea
Binomials
Example:7x + 4 Linear9x4 +11 4th
degree
Number of terms:Two = “bi”7x + 4
Degree:The degree of monomial with greatest degree
Main idea
Trinomials
Example:3x2 + 2x + 1 Quadratic
Number of terms:Three =”tri”3x2 + 2x + 1
Degree:The degree of the monomial with greatest degree
Main idea
Polynomials
Example:3x5 + 2x3 + 5x2 + x - 45th degree
Number of terms:Many (> three) =”poly”
Degree: The degree of the monomial with greatest degree
Why are these steps important?
Factor A2 - C2
“DOTS” = Difference of Two Squares
Check for DOTS in DOTS 3(x2 + 4 ) ( x2 - 4)3(x2 + 4 ) ( x + 2)(x - 2)
Check using FOIL.
Step 5
Write the numbers and variables before they were squared in the binomials. (Note: Any even power on a variable is a perfect square. . . just half the exponent when factoring) x2 + 4 ) ( x2 - 4)3(
Step 4
Example: 3x4 - 48Factor out the GCF. 3( x4 – 16)
Check for : 1.) 2 terms 2.) Minus Sign
3.) A and C are perfect squares
Write two binomialsSigns: One + ; One - 3( + ) ( - )
Step 1
Step 2
Step 3
Following these steps will allow one to factor any polynomial that is not prime.
Factoring a quadratic trinomial enables one to determine the x-intercepts of a parabola.
Factoring also enables one to use the x-intercepts to graph.
Function notation /evaluating functions
DomainRange
Function – vertical line test
Relations and
Functions
Point-slope formy – y1 = m(x – x1)
Standard formAx + By = C
Slope-intercept formy = mx + b
Linear Equations
y = yx x
Constant of variation, k
y = kxDirect
Variation
Equation of line of best fit
Scattergram
Line of best fit or trend line
Linear Models
h is horizontal movement and k is vertical movement
Always graphs as a “V”
y = |x – h| + kVertex (h,k)
Absolute Value
Functions
If test is true, shade to include point
Graph line first – called the boundary equation
Test a point not on the line – best choice is (0,0)
Graphing Two-Variable
Inequalities
Functions, Equations, and Graphs
1 Graph the linear equations on the same coordinate plane.
2 If the lines intersect, the solution is the point of intersection.
3 If the lines are parallel, there is no solution.
4 If the lines coincide, there is infinitely many solutions.
1Solve one of the linear equations for one of the variables (look for a coefficient of one).
2Substitute this variable’s value into the other equation.
3Solve the new equation for the one remaining variable.
4Substitute this value into one of the original equations and find the remaining variable value.
1Look for variables with opposite or same coefficients.
2If the coefficients are opposites, add the equations together. If the coefficients are the same, subtract the equations, by changing the sign of each term in the 2nd equation and adding.
3Substitute the value of the remaining variable back into one of the orig. equations to find the other variable.
1 Choose a variable to eliminate.
2 Look the coefficients and find their LCD. This is the value you are trying to get.
3 Multiply each equation by the needed factor to get the LCD.
4 Continue as for regular elimination
GRAPHING SUBSTITUTION ELIMINATION ELINIMATION VIA MULTIPLICATION
The solution (if it has just one) is an ordered pair. This point is a solution to both equations and will test true if substituted into each equation.
Method 1 Method 4Method 3Method 2
SUMMARY
TopicSolving Systems of Linear Equations
Finding solutions for more than one linear equation by using one of four methods.
Main Idea
Details
Five (5)
If a number ends withO or 5
Topic
Details
Divisibility
Dividing numbers that don’t have remainders
Main Idea
Details
Two (2)
If a number ends withO, 2, 4, 6, 8
Main Idea
Details
Ten (10)
If a number ends with O
Main Idea
Details
Nine (9)
If the sum of the digits can be divided by 9
Main Idea
Details
Three (3)
If the sum of the digits can be divided by 3
Exponents are important for the graduation exam. Exponents are also used in exponential functions which model population growth, compound interest, depreciation, radio active decay, and the list goes on an on. . . . .
So what? What is important to understand about this?
Exponent Rules
Zero Exponents
n0 = 1-n0 = -1(-n) 0 = 1
Negative Exponents
n-1 = 1/n1/n-1 = n
Multiplying Like Bases
am an = am + n
Power to a Power
(am)n = amn
Product to a Power
(ab)n = an bn
Dividing Like bases
am = am-n
an
Quotient to a Power
(a/b)n = an/ bn
Synonyms Intersection, Overlap, Common, Same
Union, Every, AllMain ideas
Comparing….
So what? What is important to understand about this?
Topic Topic
Graph----------│----------------│--------------- -4 0 1
----------│-----│----------│--------------- --2/3 0 5
And Or
To solve real world problems involving chemistry of swimming pool water, temperature, and science.
Notation2x + 3 < 5 and 2x + 3 > -5
-5 < 2x + 3 < 5
3x – 2 > 13 or 3x – 2 < - 4
TOPIC Order of Operations - What we should do in an equation situation…AHSGE: I-1 Apply order of operations
Main Idea
Details
PLEASE
Parenthesis Do all parentheses first.
Main Idea
Details
EXCUSE
ExponentsDo all exponents second.
Main Idea
Details
MY
Multiplication Do all multiplication from left to right next.
Main Idea
Details
DEAR
Division Do all division from left to right next.
Main Idea
Details
AUNT
AdditionDo all addition from left to right.
Main Idea
Details
SALLY
Subtraction Do all subtraction from left to right.
Note: Complete multiplication and division from left to right even if division comes first. Complete addition and subtraction from left to right even if subtraction comes first.
Polynomial ProductsMultiplying Polynomials and Special Products
So what? What is important to understand about this?
AHSGE Objective: I -3. Applications include finding area and volume. Special products are used in graphing functions by hand. Punnett Squares in Biology.
Main idea
Polynomial times Polynomial
Monomial times a Polynomial: Use the distributive property Example:-4y2 ( 5y4 – 3y2 + 2 ) = -20y 6 + 12y 4 – 8y2 Polynomial times a Polynomial:Use the distributive PropertyExample: (2x – 3) ( 4x2 + x – 6) = 8x3 – 10x2 – 15x + 18
Main idea
Binomial times Binomial
FOIL: F = FirstO = OuterI = InnerL = Last
Example: (3x – 5 )( 2x + 7)=6x2 + 11 x - 35
Main idea
Square of a Binomial
(a + b) 2 = a2 + 2ab + b2
(a – b) 2 = a2 – 2ab + b2
1st term: Square the first term 2nd term: Multiply two terms and Double 3rd term: Square the last term
Example: (x + 6)2 = x2 + 12 x + 36
Main idea
Difference of Two Squares
DOTS: (a + b) ( a – b) = a2 – b2
Example: (t3 – 6) (t3 + 6) = t6 – 36
These are the steps to …Factor A2 - C2
“DOTS” = Difference of Two Squares
Five StepsCopyright 2003 Edwin Elliswww.GraphicOrganizers.com
Check for DOTS in DOTS 3(x2 + 4 ) ( x2 - 4)3(x2 + 4 ) ( x + 2)(x - 2)
Check using FOIL.
Step 5
Write the numbers and variables before they were squared in the binomials. (Note: Any even power of a variable is a perfect square. Just half the exponent when factoring) 3(x2 + 4 ) ( x2 - 4)
Step 4
Five Steps
Example: 3x4 - 48Factor out the GCF. 3( x4 – 16)
Check for : 1.) Two terms 2.) Minus Sign 3.) A and C are perfect squares
Write two binomialsSigns: One + ; One - 3( + ) ( - )
Step 1
Step 2
Step 3
Name
AHSGE : I – 4 Factor Polynomials.
Why are these steps important?
Following these steps will allow one to factor any binomial that is not prime.
Factoring a quadratic trinomial enables one to determine the x-intercepts of a parabola.
These are the steps to …Factor Ax2 + Bx + CTrial and Error.
Five StepsCopyright 2003 Edwin Elliswww.GraphicOrganizers.com
Check using FOIL. 8(3x2 – 3x – x + 1) =8(3x2 – 4x + 1) =24x2 – 32 x + 8
Step 5
If C is positive, determine the factor combination of A and C that will add to give B. If C is negative, determine the factor combination of A and C that will subtract to give B. Since C is positive add to get B: 8 (3x – 1) (x – 1)
Step 4
Five Steps
Example: 24m2 – 32m + 8Factor out the GCF 8(3m2 – 4 m + 1)
Write two binomialsSigns: +C -- signs will be the same sign as the sign of B -C -- signs will be different: one negative and one positive 8( - ) ( - )
List the factors of A and the factors of C.A = 3 C = 1 1, 3 1, 1
Step 1
Step 2
Step 3
Name
AHSGE: I – 4 Factor Polynomials.
Why are these steps important?
Following these steps will allow one to factor any trinomial that is not prime.
Factoring a quadratic trinomial enables one to determine the x-intercepts of the parabola.
These are the steps to …Factoring Polynomials Completely Five Steps
Copyright 2003 Edwin Elliswww.GraphicOrganizers.com
Make sure that each polynomial is factored completely.If you have tried steps 1 – 4 and the polynomial cannot be factored, the polynomial is prime.
Step 5
Four Terms: Grouping Group two terms together that have a GCF. Factor out the GCF from each pair. Look for common binomial. Re-write with common binomial times other factors in a binomial.Example: 5t4 + 20t3 + 6t + 24 = (t + 4) (5t3 + 6)
Step 4
Five Steps
Factor out the GCFExample: 2x3- 6x2= 2x2( x – 3)Always make sure the remaining polynomial(s) are factored.
Two Terms: Check for “DOTS” A2 – C2 (Difference of Two Squares) Example: x2 – 4 = (x – 2 ) (x + 2) See if the binomials will factor again. Check Using FOIL
Three Terms: Ax2 + Bx + C Check for “PST” m2 + 2mn + n2 or m2 – 2mn + n2. Factor using short cut. No “PST”, factor using trial and error. Example PST: c2 + 10 c + 25 = (c + 5)2 For an example of trial and error, see Trial/Error Method.
Step 1
Step 2
Step 3
Name
AHSGE: I – 4Factoring Polynomials.
Why are these steps important?
Following these steps will allow one to factor any polynomial that is not prime.
Factoring allows one to find the x-intercepts and in turn graph the polynomial.
Projectile
Trajectory
Gravity
Vocabulary -- Define and give an example
Acceleration due to gravity
More Vocabulary
Parabola
Fill in the blank. Horizontal and vertical motions are ___________( independent/ dependent) of each other.
When was the snowboard invented?
What is “goofy foot”? What is regular foot?
What is “hang time”?
Snowboarding
Where does hang time occur on a parabola?
Which motion is affected by gravity?
Name sports that involve parabolas.
Snowboarding and its relationship to math
Is about …Big Air Rules
Standard form: ax2 + bx + c = 0
Quadratic Formula
Pythagorean Theorem
c = longest side
Distance Formula
Two points: (x1,y1) (x2,y2)
Two points: (x1,y1) (x2,y2)
MidpointFormula
RADICAL FORMULAS
Most of these formulas involve simplifying a radical.
Topic
Applications: Finding the center of a circle, finding the perimeter of a figure, finding the missing side of a right triangle, solving quadratic equations are all areas where these problems are used in real-world situations.
Q: Why should I know how to use these formulas?A: They are on the exit exam as well as in geometry and higher level math courses.
2 4
2
b b ac
a
2 2 2a b c 2 22 1 2 1( ) ( )x x y y
1 2 1 2,2 2
x x y y
Conditional
An if-then statement If an angle is a straight angle, then its measure is 180.
p → q If p, then q.
Term
Definition Example Symbolic form/read it
Negation (of p)
Has the opposite meaning as the original statement.
An angle is NOT a straight angle.
~pNOT p.
Term
Definition Example Symbolic form/read it
Inverse
Negates both the if and then of a conditional statement
If an angle is NOT a straight angle, then its measure is NOT 180.
~p → ~qIf NOT p, then NOT q.
Term
Definition Example Symbolic form/read it
Contra-positive
Switches the if and then and negates both.
If an angle’s measure is NOT 180, then it is NOT a straight angle.
~q → ~pIf NOT q, then NOT p.
Term
Definition Example Symbolic form/read it
Name ___________________Conditional
An if-then statement If an angle is a straight angle, then its measure is 180.
The part following the if is the hypothesis and the part following the then is the conclusion.
p → qIf p, then q.
Term
Definition Example Symbolic form/read it
Converse
Switches the if and then of a conditional statement
If the measure of an angle is 180, then it is a straight angle.
q → pIf q, then p.
Term
Definition Example Symbolic form/read it
Bi-conditional
The combination of a conditional statement and its converse; usually contains the words if and only if.
An angle is a straight angle if and only if its measure is 180.
p ↔ qp if and only if q.
Term
Definition Example Symbolic form/read it
Term
Definition Picture Knowledge Connection
The ratio of the sides is 1 : 2: √3
Side opposite the 30º angle = ½ hypotenuse
Side opposite the 60º angle = ½ hypotenuse times √3
The larger leg equals the shorter leg times √3
30º- 60º- 90º
45º- 45º- 90º
The ratio of the sides is 1 : 1 : √2
Side opposite the 45º angle = ½ hypotenuse times √2
Hypotenuse = s √2 where s = a leg
Is about …Special Right Triangles
30°
60°
45°
45°
Math Curseby Jon Scieszka + Lane Smith
How do you get to school in the morning? What time do you leave and what time do you arrive? If you were 15 minutes late leaving your house for school, what time would you arrive? What would you not have time to do if you were late and why?
If there were approximately 1300 students in the school, how many fingers would there be? How would you write that in scientific notation?
If an M&M is about a centimeter long, then how many M&Ms long is your foot?
If he bought an 80cent candy bar that was on sale for 25% off, how much would he have to pay? Would it be more or less than the candy bar that was on for sale for 50% off? Explain.
Title
1.
2.
3.
4.
Writing Linear Equations …
Three Forms of a Linear Equation
Main Idea
Details
1. Given slope = m , and y-int= b
2. Substitute m and b into the
equation.
3. Transform to Standard if necessary.
Slope-Intercept Form
Y = mx + b
Main Idea
Details
1. Given an equation in slope-
intercept form. a. Eliminate fractions b. Add or Subtract
2. Given an equation in point-slope form.
a. Distribute b. Eliminate Fractions c. Add or Subtract
Standard Form
Ax + By = C
Main Idea
Details
1. Given slope = m&point (x1, y1)
Substitute m and the point into the equation.
2. Given 2 points a. Find m b. Substitute into point slope form c. Simplify/change to
Slope- intercept or Standard form if necessary.
Point-Slope Form
y – y1 = m(x – x1)
So what? What is important to understand about this?
Many real life situations can be described by an equation, for instance, payroll deductions, temperature . . .