Chapter 10 Rules

Linear Equation

An equation whose graph is a line, variables cannot be multiplied or divided by each other, and cannot be exponential or a radical

Slope

Rise over run

Slope Formula

(y₂- y₁) / (x₂- x₁)

Slope Intercept Form

y\=mx+b

Point Slope Form

y-y1\=m(x-x1)

Standard Form

Ax+By\=C

Y Intercept

the y-coordinate of a point where a graph crosses the y-axis (0,y), to find: set the x to zero

X Intercept

the x-coordinate of a point where a graph crosses the x-axis, (x,0) to find: set the y to zero

Writing Slope Intercept Given Two Points

Find the slope, and plug in a point to find the y intercept (b), then write the formula

Parallel Slopes

Exact same slope

Perpendicular Slope

Opposite reciprocal

Solving a System of Equations by Elimination

Set the two equations under each other, and eliminate one of the variables. ex. y\=13x+6 and y\=-13x+9. Then "add" them together.

Solving a Systems of Equations by Substituition

Isolate one of the variables, then plug it into the other equation.

Results of a Radical

Both positive and negative

Solving an Absolute Value

Isolate the absolute value, then set up two equations, one with a positive and one with a negative on the other side.

Solving an Inequality

When multiplying or dividing both sides by a negative number, always change the inequality sign (i.e. if it was < then change it to \>, if it was \> then change it to

Graphing an Inequality

≤or≥ is a closed dot,

Exponent Product Rule

a^m*a^n\=a^m+n

Exponent Quotient Rule

a^m/a^n\=a^m-n

Exponent Zero Rules

Any number or variable to the power of zero is one.

Negative Exponent

x^-n\=1/x^n

(a/b)^n\=a^n/b^n

(a^m)^n\=a^mn

Arithmetic Sequence Formula

an\=a1+(n-1)d, where d is the common difference

Geometric Sequence Formula

an\=a1(r)^n-1, where r is the common ratio

Distance Formula

d \= √[( x₂ - x₁)² + (y₂ - y₁)²]

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

Pythagorean Theorem

a²+b²\=c²

Linear Function

A function whose graph is a straight line, same slope, and no repeated x values.

Distributive Property

a(b + c) \= ab + ac

Commutative Property

a+b\=b+a

Associative Property

(a+b)+c\=a+(b+c)

Identity Property

a+0\=a or a*1\=a

Exponential Growth Equation

f(x)\=a(b)^x, where a is the 1st term, b is the common ratio, and x is the amount that you are multiplying by

Real Numbers

the set of all rational and irrational numbers

Irrational Number

a number that can NOT be expressed as a ratio of two integers or as a repeating or terminating decimal - Pi or any square root of an imperfect square are considered irrational

Rational Number

A number that can be written as a fraction

Natural Number

The set of numbers 1, 2, 3, 4, ... Also called counting numbers.

Integer

All whole numbers (both positive and negative) and zero.

Whole Numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

Scatter Plot

A graph with points plotted to show a possible relationship between two sets of data.

Correlation/Relationship

Relationship between two data set

Positive Correlation

Relationship betwen data increases as you read from left to right

Negative Correlation

Data decreases as you read from left to right

No Correlation

Cannot make sense of the graph. (Like someone went to JoAnn fabrics, grabbed some glitter, and dumped it all over the graph)

Trend Line/Line of Best Fit

Helps show the correlation more clearly, should be as close to all points, and divide the points about evenly. Does not have to start at the origin, and can be drawn with a slope-intercept equation.

Scientific Notation

A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.

Wind Speed

When going against the wind, subtract, when going with the wind, add.