Tangent and Slope of Lines
Slope of a Line Passing Through the Origin
If a line passes through the origin then the equation for that line will take the form:
(1)\begin{equation} y=mx \end{equation}
Slope is defined as:
(2)\begin{align} slope=\frac{rise}{run}=\frac{y_2 - y_1}{x_2 - x_1} \end{align}
If we use the origin as one of those points we can see that:
(3)\begin{align} slope=\frac{y}{x}=tan \theta \end{align}
The IB loves this detail. It shows up once every 3-4 years. The slope of of line that goes through the origin can be written:
(4)\begin{align} y= tan(\theta) \cdot x \end{align}
The questions involving this idea are generally simple and mostly require a student to remember this or derive it, but frankly you don't have time to derive…
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page revision: 4, last edited: 06 Feb 2013 19:38
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