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Grade 9/Math/MFM1P1/Final_Exam_Study_Sheet.md
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## Interpreting Scatter Plots ## Interpreting Scatter Plots
- A scatterplot graph is there to show the relation between two variables in a table of values. - A scatterplot graph is there to show the relation between two variables in a table of values.
- A line can be drawn through the most concentrataed points, to show a trend. - A line can be drawn through the most concentrataed points, to show a trend.
- - Given a value, to find the other value, use follow the line that the dot is on and check the value on the other axis. For example, if a point is on `(1, 2)`, if you are given `2`, to get `1`, just following the vertical line to find the corresponding number on the `x-axis`.
- <img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/line%20of%20best%20fit-eyeball/lineofbestfit-e-1.gif" width="300"> - <img src="https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/line%20of%20best%20fit-eyeball/lineofbestfit-e-1.gif" width="300">
## Line Of Best Fit ## Line Of Best Fit
- A line that represents the `trend` in a graph.
### How To Find The Line of Best Fit ### How To Find The Line of Best Fit
1. Find two points **```ON```** the ```line of best fit``` 1. Simply draw the line according to the properties of the line below.
2. Determine the ```slope``` using the two points 2. Use a ruler when drawing the line.
3. Use ```point-slope form``` to find the equation of the ```line of best fit``` 3. Make sure the line of best fit represents the trend.
### Properties Of Line Of Best Fit ### Properties Of Line Of Best Fit
- Shows the trend for the data in a scatter plot. - Shows the trend for the data in a scatter plot.
- Shows the pattern and direction of the data points. - Shows the pattern and direction of the data points.
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- Remaining points should be grouped equally above and below the line and spread out along the line. - Remaining points should be grouped equally above and below the line and spread out along the line.
- Helps make predictions for values not actually recorded and plotted. - Helps make predictions for values not actually recorded and plotted.
## Curve Of Best Fit
- A curve that represents the `trend` in a graph.
### How To FInd The Curve Of Best Fit
1. Simply draw a curve that connects all the points.
2. You can also use an online graphing calculator, like [DESMOS](https://www.desmos.com/calculator).
## Time - Distance Graph ## Time - Distance Graph
- Time is the independent variable and distance is the dependent variable - 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 - You can't go backwards on the x-axis, as you can't go back in time
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2. ```going away from home``` 2. ```going away from home```
3. ```stop``` 3. ```stop```
## Graphing Linear Relations
- A linear relation is a `straight line`.
### Graphing Using Table Of Values
- To graph the relation, first look at the `Table of Values`.
- Then decide which columns are the x and y axis.
- Then do a scatter plot/graph, where the numbers are the points.
- Example:
- Given the table of values:
- |Hours Worked|Pay in dollars|
|:--|:-----|
|3|100|
|6|200|
|9|300|
|12|400|
- First label the x and y axis, since time is the **independent variable**, the `Hours Worked` will be `x-axis`. The `Pay in dollars` will be our y-axis.
-