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+# Unit 5: Analytical Geometry and Linear Relations
+- ```Linear Relation```: A relation which a single straight line can be drawn through every data point and the first differences are constant
+- ```Non - Linear Relation```: A single smooth curve can be drawn through every data point and the first differences are not constant
+
+## Slope and Equation of Line
+- ```Slope```: The measure of the steepness of a line - ```rise / run``` or ```the rate of change```
+- ```Slope Formula```: $`m = \frac{y_2 - y_1}{x_2 - x_1}`$
+- ```Standard Form```: $`ax + by + c = 0, a \isin \mathbb{Z}, b \isin \mathbb{Z}, c \isin \mathbb{Z}`$ (must be integers and $`a`$ must be positive)
+- ```Y-intercept Form```: $`y = mx + b`$
+- ```Point-slope Form```: $`y_2-y_1 = m(x_2-x_1)`$
+- The slope of a vertical lines is undefined
+- The slope of a horizontal line is 0
+- Parallel lines have the ```same slope```
+- Perpendicular slopes are negative reciprocals
+
+## Relations
+- A relation can be described using
+ 1. Table of Values (see below)
+ 2. Equations $`(y = 3x + 5)`$
+ 3. Graphs (Graphing the equation)
+ 4. Words
+- When digging into the earth, the temperature rises according to the
+- following linear equation: $`t = 15 + 0.01 h`$. $`t`$ is the increase in temperature in
+- degrees and $`h`$ is the depth in meters.
+
+## Perpendicular Lines
+- To find the perpendicular slope, you will need to find the slope point
+- Formula: slope1 × slope2 = -1
+- Notation: $`m_\perp`$
+- 
+
+
+## Definitions
+- ```Parallel```: 2 lines with the same slope
+- ```Perpendicular```: 2 lines with slopes that are the negative reciprocal to the other. They form a 90 degree angle where they meet.
+- ```Domain```: The **ordered** set of all possible values of the independent variable $`x`$.
+- ```Range```: The **ordered** set of all possible values of the dependent variable $`y`$.
+- ```Continous Data```: A data set that can be broken into smaller parts. This is represented by a ```Solid line```.
+- ```Discrete Data```: A data set that **cannot** be broken into smaller parts. This is represented by a ```Dashed line```.
+- ```First Difference```: the difference between 2 consecutive y values in a table of values which the difference between the x-values are constant.
+- ```Collinear Points```: points that line on the same straight line
+
+## Variables
+- ```Independent Variable```: A Variable in a relation which the values can be chosen or isn't affected by anything.
+- ```Dependent Varaible```: A Variable in a relation which is **dependent** on the independent variable.
+
+## Statistics
+- ```Interpolation```: Data **inside** the given data set range.
+- ```Extrapolation```: Data **outside** the data set range.
+- ```Line of Best Fit```: A line that goes through as many points as possible, and the points are the closest on either side of the line,
+- and it represents the trend of a graph.
+- ```Coefficient of Correlation```: The value that indicates the strength of two variables in a relation. 1 is the strongest and 0 is the weakest.
+- ```Partial Variation```: A Variation that represents a relation in which one variable is a multiple of the other plus a costant term.
+
+## Time - Distance Graph
+- Time is the independent variable and distance is the dependent variable
+- You can't go backwards on the x-axis, as you can't go back in time
+- Plot the points accordingly
+- Draw the lines accordingly
+- 
+
+**Direction is always referring to:**
+
+ 1. ```go towards home```
+ 2. ```going away from home```
+ 3. ```stop```
+
+## Scatterplot and Line of Best Fit
+- A scatterplot graph is there to show the relation between two variables in a table of values.
+- A line of best fit is a straight line that describes the relation between two variables.
+- If you are drawing a line of best fit, try to use as many data points, have an equal amount of points onto and under the line of best fit, and keep it as a straight line.
+- 
+
+### How To Determine the Equation Of a Line of Best Fit
+ 1. Find two points **```ON```** the ```line of best fit```
+ 2. Determine the ```slope``` using the two points
+ 3. Use ```point-slope form``` to find the equation of the ```line of best fit```
+
+## Table of values
+- To find first differences or any points on the line, you can use a ```table of values```
+
+ | y | x |First Difference|
+ |:--|:--|:---------------|
+ |-1|-2|.....|
+ |0|-1|(-1)-(-2) = 1|
+|1|0|0 - (-1) = 1|
+|2|1|1 - 0 = 1|
+|3|2|2 - 1 = 1|
+|4|3|3 - 2 = 1|
+
+## Tips
+- Label your graph correctly, the scales/scaling and always the ```independent variable``` on the ```x-axis``` and the ```dependent variable``` on ```y-axis```
+- Draw your ```Line of Best Fit``` correctly
+- Read the word problems carefully, and make sure you understand it when graphing things
+- Sometimes its better not to draw the shape, as it might cloud your judgement (personal exprience)
+- Label your lines
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