3A - Gradients and angles
3A - Content video: The gradient of a straight line
This video covers the theory and an examples relating to the gradient of a straight line.
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■ For a line passing through two points, \((x_1 , y_1)\) and \((x_2 , y_2)\), the gradient is given by \[m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}\]
The gradient, \(m\), is essentially the slope of the line. Gradients can be:
3A - Content video: Angles created by a line
This video covers the theory and an examples relating to the angles created by a line.
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Straight lines create an angle, \(\theta\), with the positive \(x\)-axis. \[tan(\theta)=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=m\]
■ Therefore, the angle created by a line with gradient \(m\) is given by \[\theta=tan^{-1}(m)\]
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