Download Do You Remember (part 1)…

Do You Remember (part 1)….
Linear Functions
y=mx+b
m- slope;
b- y-intercept
REMEMBER: y needs to be by itself to find m and b
Solving Equations for Y (Ch. 5, Sect. 6, Example 3)
If looking at an equation then, put into the form y = mx + b, then look for the value that’s in place of the m.
Ex. 5x-3y=15
Always move the ‘x’ 1st if it is on the same side of the ‘y’ by doing the opposite.
-3y = 15-5x
Then divide if ‘y’ still isn’t by itself.
5
Y = -5+ x
3
5
So, the slope is .
3
(Ch. 5 Sect 8)
Parallel: when two lines have the same slope (the m is exactly the same)
Example:
y=2x+4
y=2x-8
These two lines are parallel
Perpendicular: When two lines have slopes that are opposite reciprocals (the fraction is flipped and the sign is
changed)
5
2
y  x2
y   x  4 These lines are perpendicular
Example:
2
5
When given a point ( x1 , y1 ) and a slope ( m) , use the point-slope formula: y  y1  m( x  x1 )
System of Equations (Ch. 6)
A solution is where the two lines intersect.
Method
Graphing
Circle Substitution
Elimination
What is by itself
Both Y’s
One variable
No variables
y  2x  2
x  3y  2
1
y  x4
2
x  2y  8
Example
2 x  3 y  10
x  3 y  2
Graphing:
Find m and b (y=mx+b) and plot on a graph
You can use this method on ANY problem as long as you solve for Y
Circle Substitution:
1. After circling the variable by itself write down the other equation.
2. Draw an arrow from the circled variable to the matching variable in the other equation.
3. Take out that variable and replace with parentheses.
4. Inside the parentheses write the other side of the equation of the circled variable.
5. Solve and plug answer back into the circled equation.
Elimination:
1. Make sure that a variable will cancel out (needs to have same number AND different signs).
a. If they do not have different signs- multiply one EINTIRE equation by -1.
b. If they do not have the same number- find the least common multiple and multiply the entire equation
by that number.
2. Once a variable has the same number and different signs, add both equations together.
3. Solve and select the easiest looking equation to plug your answer back in to in order to find both variables.
If you do not want to use this method: solve for y on both equations and use the graphing method.
Word Problems For Systems
You will always need two equations. Usually each sentence describes an equation.
X and Y-Intercepts (Ch.5 Sect.2)
x-intercept is when y=0. Plug 0 in for y and solve for x.
y-intercept is when x=0. Plug 0 in for x and solve for y.
Graphing Inequalities (Ch. 6 Sect. 5)
1. Find b (y-intercept) and m (slope- rise over run)
2. Plug them into y ? mx+b
3. For the ? :
put a  if the shading is above a solid line or a  if the shading is above a dashed line
put a  if the shading is below a solid line or a < if the shading is below a dashed line
Do You Remember (part 2)….
Definitions (Ch. 7-5):
 Monomial- one term
 Binomial- two terms
 Trinomial- three terms
 Polynomial- four or more terms
 Degree- the largest exponent of a polynomial
 Descending order- ordering a polynomial from the term that has the largest exponent to the smallest
exponent
 Linear function- has a degree of one
 Quadratic function- has a degree of two
 Cubic function- has a degree of three
Simplifying Polynomials (Ch.7 Sect. 6)
1. When there are parentheses, be sure to distribute.
2. Combine like terms (check exponents to be sure they are the same too)
3. Put in descending order
Properties of exponents (Ch. 7 Sect. 3&4)
Expand variables according to the exponent
Ex. x 4  x  x  x  x
If multiplying count how many there are and use that as the exponent
Ex. x3  x 2  x  x  x  x  x  x5
If dividing, cancel out.
x6 x  x  x  x  x  x

 x4
2
x
xx
If there is a number outside the parenthesis, write out that many parentheses.
Ex.
Ex. (2 x 4 )3  (2 x 4 )(2 x 4 )(2 x 4 )
Multiply numbers with numbers and variables with variables.
Ex. (3x 2 )(2 x3 )  2  3  x  x  x  x  x  6 x5
A negative exponent means it is on the “wrong side”
x3
y5
Anything raised to the power of 0 equals 1.
Ex. x3 y 5 
When two binomials are multiplied together (Ch. 7 Sect. 7),
use the box method, distributive method or FOIL.
Box Method:
Foil Method: Ex: (2x+3)(x-8)
Put parentheses on the outside of box
F(first terms multiply) 2x∙x= 2x 2
Ex: (2x+3)(x-8)
O(outside terms multiply) 2x∙-8= -16x
2x
+3
x
I (inside terms multiply) 3∙x=3x
L(last terms multiply) 3∙-8= -24
-8
Bring numbers to the inside and multiply.
x
2x
+3
2x2
3x
-8 -16x -24
Take the terms from the inside and list them in order.
2x2 +3x -16x -24
Combing like terms.
2x2-13x-24
Ex: (2x+3)(x-8) See above
2 x 2  16 x  3x  24  2 x 2  13x  24