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Chapter 6 - Linear Graphs and Models - Coggle Diagram
Chapter 6 - Linear Graphs and Models
6A - Plotting straight line graphs
Any equation that is of the form (y = a + bx) will graph as a straight line. (Linear relationship)
The slope (gradient) of the line is constant
Check CAS instructions
6B - What is the slope
The slope is a measure of how high it rises in comparison to how far is travelled horizontally. The larger the slope the steeper the line.
Rises from Left --> right = positive slope
Falls from left --> right = negative slope
A horizontal line has no slope
A vertical line, the slope is not defined.
6C - The general equation
The intercept-slope form ( y = a + bx )
Finding the slope and y-intercept
Sketching the graph
6D,E,F - finding the equation
Using the intercept slope form
Look at the graph and find the y-intercept and work out the slope
Passes through points
Using the points find the slope --> y2 - y1 / x2 -x1
After finding the slope use one of the points (x) preferably lowest and the gradient to find y-intercept
Use CAS
6G - Linear Modelling
Linear modelling refers to situations in real like where the relationship between two variables can be measured.
If, the rate of
__
is constant then it can be modeled by the linear equation
Predictions can be made from linear modelling
Line of best fit
When a straight line does not exactly fit a set of data, we draw a line of best fit
When line of best fit is used, we use points on line of best fit and not given data
Interpolation -- > Using a model to make a prediction within the range of data given to further construct a model. It is fairly reliable
Extrapolation --> Using a model to make a prediction outside a data range. Less reliable as we have no way of knowing if the model continues beyond the data.
Picewise linear graph --> More than one slope on a graph. Different segments.