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When two lines are crossed by another line (which is called the Transversal), the pairs of angles:
• on opposite sides of the transversal
• but outside the two lines

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When two lines are crossed by another line (which is called the Transversal), the pairs of angles
• on opposite sides of the transversal
• but inside the two lines

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the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

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Angles are are next to each other
Adjacent angles are supplementary, both angles combined should equal 180.

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A Pair of Parallel Lines Cut by a Transversal

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A Pair of Parallel Lines Cut by a Transversal

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A Dilation is when an image gets smaller or larger
A scale factor greater than one means that the image will be enlarged.
A scale factor less than one will shrink.

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A Rotation is known as a turn of a figure
A Counter Clockwise Rotation of 90 degrees follows the rule (x,y)->(-y,x) a clockwise rotation of 270 is the same as this.
A Rotation of 180 degrees follows the rule (x,y)->(-x,-y)
A counterclockwise rotation of 270 degrees follows the rule (x,y)->(y,-x) which is also the same as a clockwise rotation of 90 degrees

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A Reflection is known as a flip of a image.
When a Reflection is done over the x-axis, the y-value is negated,
When an image is reflected over the y-axis, the x-value is negated.

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A translation is known as a slide of a figure
Normally a translation rule is given by the change in the x-value, and a change in the y-value (x+#,y+#)

1. X-value-if the number is being added it is a slide to the right, if it is negative it is a slide to the left.

2. Y-Value-if the number is positive it is a slide up, if the number is negative it is a slide down.

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Both equations should have the same coefficient but different sign.
If they do not you need to find which what number you can multiply by to give you similar variables
Combine both variables
Solve for the remaining variable
Substitute the solution to the variable into one of the original equations
Check both variables with one of the original equations.

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1. Rewrite both lines in slope intercept form(y=mx+b)

2. Graph both lines, remember to label the x-axis,y-axis, the lines you graph.

3. Where the two lines intersect is where the solution will be

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1. Solve one equation for one of the variables

2. Replace the variable with equation found

3. Solve the new equation for the remaining variable

4. Substitute thevalue into either original equation

5. check both variables in both equations

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y=mx+b is known as slope intercept form.
y stands for the y value
m is the slope
x is the x-value
and b is the y-intercept

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A relation in which ever x-value(domain) is paired with one and only one y-value.
When look at a graph a good way to see confirm if it is a function is the use of the vertical line test.

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The y-value or second number of an ordered pair.
ex. (0,1),(2,3) 1 and 3 are the range

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the x-value or first number in an ordered pair.
ex. (0,1), (2,3) 0 and 1 are the domain

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A set of ordered pairs
ex. (0,1),(2,3)

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Look at slope from left to right

If the solution is going up it is increasing and has a positive slope

If the line is going down it is decreasing and has a negative slope

A horizontal line has a slope of 0

A vertical line has an undefined slope(This is also not a function).

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1. A linear equation has one solution, if x can be equal to only one number.

2. A linear equation has infinitely many solutions  if two numbers equal each other or both sides of the equation are identical

3. A linear equation has no solution if there are two numbers that are equal to each other or, the coefficient is the same but constant is different.

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Solving Equations with Variables on Both Sides

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Solving Equations with Variables on Both Sides

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1. Distribute (get rid of fractions)

2. Combine Like Terms

3. Add or Subtract

4. Multiply or Divide

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Solving Multi-Step Equations with Variable on One Side

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Solving Multi-Step Equations with Variable on One Side

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1. Distribute(get rid of fractions)

2. Combine like terms on both sides of the equation

3. Add or Subtract on both sides

4. Multiply or Divide on both sides

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Perform the opposite operation(addition or subtraction) of the constant. Then perform the opposite operation(multiply or divide) of the coefficient.

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Solving One Step Equations Using Multiplication or Division

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Solving One Step Equations Using Multiplication or Division

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Perform the opposite operation of the coefficient.

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Solving a One Step Equation Using Addition or Subtraction

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Solving a One Step Equation Using Addition or Subtraction

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Take the constant that is on the same side as the variable. Perform the opposite operation on both sides to get the solution.

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When you multiply to multiple addends that are in parenthesis

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Changing the grouping of an expression

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You are able to move around terms that are connected by an operator.

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You can combine like terms if they have the same variable

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1. Group the coefficients together and the numbers of base 10 together.

2. Divide the coefficients while you subtract the exponents of the numbers of base 10.

3. Adjust the answer to be in scientific notation if necessary.

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1. Group the coefficients together and the numbers with base 10 together.

2. Multiply the coefficients together and the numbers of base 10 together.

3. If necessary change to scientific notation if the answer is not already in scientific notation

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Adding and Subtracting in Scientific Notation

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Adding and Subtracting in Scientific Notation

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1. Convert the number to standard form

2. Perform the operation

3. Convert the number back to Scientific Notation

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A number written out in an expanded form.
Examples:
524
6702
.00245

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A positive, finite decimal that is expressed as a product of a number times 10 to an exponent, where the number is equal or greater than 1 but less than 10 and the exponent is an integer.

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When a number has a negative exponent, put the base in the denominator with the exponent making it positive.

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Any number raised to a 0 power is 1

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When more than one number/variable is being raised to an exponent, you distribute the power.
If the number has no exponent, the exponent is 1

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Numbers in Exponential Form Raised to a Power

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Numbers in Exponential Form Raised to a Power

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When a number is in exponential form and it is raised to a power, you multiply the exponents.

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When dividing numbers in exponential notation, keep the base and subtract the exponents.

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When multiplying keep the base and add the exponent.

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The base is the number that is being multiplied, the exponent is the number of times the base is being multiplied by.

The exponent can be found a little above and to the right of the number.

The example below, 4 is the base and 5 is the exponent.

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1. When dividing two positive numbers, the quotient will be positive.

2. When dividing two negatives, the quotient will be positive

3. When dividing a negative and a positive the quotient will be negative.

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1. If both signs are positive, the product will be positive.

2. If both signs are negative, the product will be positive.

3. If one sign is negative and the other is positive, the product will be negative.

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When subtracting integers

1. If the numbers are both positive, keep the sign of the larger number and find the difference

2. If the numbers are both negative, change the 2nd negative to a positive, keep the sign of the larger number and find the difference.

3. If there are two negatives being subtracted, change the number being subtracted to a positive, keep the sign of the larger number and find the difference

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1. When adding two numbers that are positive, keep the positive sign and add

2. When adding two negative numbers, keep the negative sign, and add

3. When adding a negative and a positive, keep the sign of the bigger number and find the difference