2B - Linear graphs
2B - Content video: Sketching linear graphs
This video covers the theory and several examples relating to sketching linear graphs.
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Linear equations:
The general form of a linear equation is \(y=mx+c\), where \(m\) is the gradient and \(x\) is the \(y\)-intercept. While it is convention to write linear equations in the form \(y=mx+c\), there are many other ways to represent a linear equations. The following are examples of linear equations:
The general form of a linear equation is \(y=mx+c\), where \(m\) is the gradient and \(x\) is the \(y\)-intercept. While it is convention to write linear equations in the form \(y=mx+c\), there are many other ways to represent a linear equations. The following are examples of linear equations:
- \(y=2x+6\)
- \(3x+5y=15\)
- \(3y-x+6=0\)
- \(x=-y+3\)
Sketching using \(x\)- and \(y\)-intercepts:
To sketch a linear graph:
To sketch a linear graph:
- Determine the \(x\)-intercept by letting \(y=0\) and solving for \(x\).
- Determine the \(y\)-intercept by letting \(x=0\) and solving for \(y\).
- Plot the \(x\)- and \(y\)-intercepts and label them with their coordinates.
- Join the \(x\)- and \(y\)-intercepts with a straight line (use a ruler).
2B - Content video: Sketching line intervals
This video covers the theory and several examples relating to sketching line intervals.
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Sketching line intervals:
To sketch a line interval between two points \((x_1,y_1)\) and \((x_2,y_2)\):
To sketch a line interval between two points \((x_1,y_1)\) and \((x_2,y_2)\):
- If necessary, determine the coordinates of the endpoints.
- Plot the endpoints and label them with their coordinates.
- Join the end points with a straight line (use a ruler).
- Determine the coordinates of any axial intercepts (if they exist).
2B - Example 1: Sketching line intervals (CAS)
Using a CAS calculator, sketch the graph of \(4y-x=8\) over the interval \(x\in [-12,8]\). Clearly label endpoints and any axial intercepts with their coordinates.
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2B - Example 1: Video solution
2B - Example 1: Practice
Question 1: ABC Question 2: ABC 2B - Example 1: Solutions
Question 1: ABC Question 2: ABC |