8th Grade Vocabulary
Current vocabulary will be in blue
Pythagorean Theorem a^2+b^2=c^2
9+ 16 = 25
It is a proof of right angles and a way to find missing triangle side lengths
distance formula sqrt((x1-x2)^2+9y1-y2)^2)
A formula derived from the pythagorean theorem to find distance of angled lines on a coordinate plane
Foil first out in last A way to multiply binomials
(x+2)(x+4) x*x + x*2
x^2 + 4x + 8
Factor A way to make a trinomial into two binomial factors
Solve system of equations Where two lines equal each other or meet.
Parallel lines No Solution Same slope different y intercepts, false statement
Infinite solutions Same line, Same slope and y intercepts, true statement
Functions For every input x there is only one output y
exponent The power something is raised to. The small numbers
Linear When graphed it is a line.
It has a constant rate of change
The exponents for x and y are 1
Proportional A line that goes through the origin (0,0)
Nonproportional A line that does not go through the origin
calculate y intercept 1st find the slope
2nd list your information
pick a point
plug in your information to y-mx to find b
3rd plug in your m and b to y=mx+b
****THE EQUATION OF A LINE in slope intercept form y=mx+b
y is dependent variable, output
m is the slope, the constant change
x in the independent variable, input
b the y intercept, where x =0, the initial value. y-mx
Module 4 Nonproportional Relationships
Non proportional relationship - When graphed it doesn't go through the orgin. The y intercept isn't 0.
Ordered Pair- (x cooridinate , y cooridinate)
Module 3 Proportional Relationships
Constant A value that doesn't change
Constant of proportionality The slope in a proportional relationship. y/x ratio will be proportional (equal constantly) for any given points on your line
Equivalent Ratios Ratio's that are equal. They are the same comparison.
Linear function When graphed its a line
Point A pair of coordinates telling you where to go on your graph. (x coordinate, y coordinate)
Proportion An equation showing two equal fractions (ratios).
Proportional relationship When graphed it will be a line that passes through the orgin (0,0). The function has a constant of proportionality. The y intercept (when x is zero) is 0. The slope is y/x.
Rate A comparison of two quantities in different units. Example; Miles per hour
Rate of change / Slope. The rate the output, (dependent variable y) changes over the rate the input (independent variable x) increases.
Slope The constant rate of change. 'M' in y=mx+b The steepness of the line. Change of output (y) /change of input (x) increasing.
Unit rate. What y is when x=1 How much one costs.
Y intercept What y equals when x = 0 Where the line crosses the y axis. 'b' in y=mx+b The initial value. The one time charge.
Module 2 Exponents and Scientific Notation
Base A number that is raised to a power.
Exponent The number that indicates the number of times the base is multiplied by itself. 'The small number'. An exponent tells what power to raise the base to.
Negative Exponent. THIS DOES NOT MEAN THE NUMBER IS NEGATIVE. You are dividing by the base raised to the given power.
Laws of exponents
Multiply Keep the base, add exponents
Divide Keep the base subtract exponents
Add or subtract The numbers must be like terms and they stay like terms. DO NOT ADD EXPONENTS WHEN ADDING.
Scientific Notation A method of writing very large or very small numbers with two factors. The first factor is a number greater or equal to 1 and less than 10. The second factor is a power of ten. If the exponent is positive the value is large. If the exponent is negative the value is very small.
Standard Notation The number not in scientific notation. The product of the two factors in scientific notation.
Operations in scientific notation.
Multiply or divide the first factors as normal, then follow laws of exponents for the second factor.
Add or Subtract. They must be like terms and they stay like terms. The 2nd factors (powers of ten) must be the same
or they are not like terms.
Decimal exponent patterns in scientific notation. Takys Rule!
If you move the decimal left add to the exponent
If you move the decimal right subtract to the exponent