Math 8 Notes

Math 8 Notes

Rules for Integers - In Algebra you are always adding - either you are adding like signs or unlike signs.
Addition
Like signs add the value and keep the sign
Different signs subtract values and keep the sign of the greater number
 *Please note that when we use the term value, we are referring to absolute value of number.

Subtraction(adding unlike signs)
To subtract an integer add its opposite or additive inverse than use the rules for addition.
(K - keep the sign of the first term)
(C - change the sign from subtraction to addition)
(F - flip the sign of the next term-use the opposite sign)


Multiplication and Division

+	-	-
-	+	-
-	-	+

Of course, positive x positive = positive
                  positive/positive = positive

When solving algebraic equations and your answer results in a negative variable, the answer is not in simplest form. Just reverse the signs on each side of the equation.

-x = 2
 x =  -2
This is not magic - you are dividing both sides of the equation by -1.
REMEMBER - just because we do not write the coefficient 1 before a variable does not mean that the 1 is not there.
-x can be written -1x

-1x = 2
   x = - 2

Math 8 Notes - Best Fit LIne

You can make predictions from an equation for a best fit line.
Write an equation in slope intercept form for the best fit line.
1. DRAW A BEST FIT LINE

2. Select two points on the line and find the slope
The two points MAY NOT be original data points. I chose 1995 (year) and 15,800 ( number of graduates) as one data point.
(1995, 15900)
Then I chose year 2000 and number of graduates as 16,100 for my second data point. 
(2000, 16100)
Find the slope  change in y over change in x
200 is change in y
5 is change in x
200/5 = 40
m= 40

Find the y intercept (b)
y = 40 x + b
15,900 = 40(1995) +b
15,900 = 79,800 + b
-63,990 = b

Write the equation
y = 40x - 63,990

Predict
y = 40(2010) + 63,990
y = 80,400 - 63,990
y = 16,400
Approximately 16,400 medical school graduates

Math 8 Notes Find the equation of a line joining (1,6) and (5,10)

Find the equation of a line joining (1,6) and (5,10)
Step 1
Identify Points
( X₁ Y₁ ) ( X₂ ,Y₂)
( 1, 6 ) (5 ,10)

Step 2
Find the slope or gradient
m = Y₂ -Y₁
        X₂ – X₁

m = 10 - 6
         5 - 1
m = 4
       4
m = 1

Slope =1

Step 3
Find the y intercept - substitute values for either of given points. I will use (1,6). Substitute value for slope (m)

y = mx + b
6 = (1) (1)+ b
6 = 1 + b
5 = b

Step 4
State equation
y = mx + b
y = 1x + 6 or y = x + 6