M8D1(A) demonstrate relation ships among sets through use if venn diagrams

Venn diagrams show the intersection of two sets of numbers
2,4,6,8,12

3,6,9,12,15

M8A4(D) Graph equations of the form ax +by=c

You can not graph anything from standard form. You have to change it to slope y intercept form then graph from there.
2x+y=4 standard
-2x   -2x
y=-2x=4 slope y-intercept

M8A3(C)ditinguish between relations that are functions and those that are not functions

Relations can have the same x value for all the y values making the line undefined
Functions don't have a repeating x value but can have a repeating y value
*You can distinguish between the two by performing a vertical line test and if the line hits the relation more than once it is not a function.

M8A1(B) simplify and evaluate algebraic expessions

-7y+4z= 7y-3z-28              combine like termes
+7y        +7y
4z=14y-3z-28
+3z      +3z
7z=14y-28                        simplify expression
 7        7
z=2y-4

M8N1 (h) distinguish between rational and irrational numbers

Rational numbers can be expressed as whole numbers, intergers decimals( repeating and terminating)
Irrational numbers can be expressed as none repeating and termianting decimals or square roots that are not whole numbers.

M8N1(J)express and use numbers in scientific notations

Scientific notations can't be more than 10 and have to be decimals. The base number is always going to be ten and the exponent represents how many numbers there are behind the decimal point.

M8N1(F) estimate square roots of postive numbers

A square root is the product of two of the same number mulipied together.
EX. 0, 4,9,16. 25. 36.49,  81 etc
To estimate the square of a postive number find the square roots that it is close. Then decide which square root it is closests to.
EX
The square root of 85
85 would be found between 81 and 100 but it is closer to 81. The square root of 81 is 9 so the best estimate would be 9 for the square root.

M8A5(C) graph the solution set of to linear inequalities in two varibles

To graph linear inequalities you have to first know what the lines should look like
greater than or equal  to and less than or equal to get solid lines
less than and grater than get dashed lines
You  have to find the intersecting point of the linear inequalities because it is part of the solution set.
To find the solution set for linear inequalities use test points such as (0,0) to find the solution set

*anything shaded is apart of the solution set and the unshaded part is not part of the solution set

M8A4(C) Graph Equations of the form y= mx+b

To graph from y =mx +b form ( slope y intercept form) you first have to graph the y intercept
 y= 2x-7 - y intercept
Then you graph the slope (2 in this equation). You also want to pay attenton to the direction of the line postive slopes go to the right and negative slopes go to the left.

M8A5(b) Solve systems of equations algebraically

There a different steps to solve equaltions such as elimination and substitution.
Substituion                                                                     Elimination

x +2y = 1                                                                      

2x-y =7 change equation to y-intercept form                   

2x-y =7                        

-2x    -2x

-y = -2x +7

-1       -1

y=2x-7

Now it’s time to substitute

x+ 2(2x-7)=1                   y=2x-7

x+4x-14   =1                    y=2(3)-7

5x-14=1                            y=6-7

  +14   +14                         y=-1

 5x =15

5           5

    x=3    To check just substitute the

              x and y values into the

              equations.

 Elimination

5x +3y =17.22      Chose which value to eliminate                   

5x+3y=17.22                                           

 3(x  - y =.90)                                             

5x+3y=17.22        eliminate the y            

3x –3y=2.70

    8x = 19.92

8                   8

  x =2.49

Solve for y

2.49-y=.90

       +y       +y  

 2.49=.90 +y

  -.90  -.90

   1.59=y

To solve by graph change the equations to slope y intercept form as shown above. Graph the y intercept first then graph the slope until the two lines meet up at one point on the graph.