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I know how to use the bisection method when finding roots, however I don't know how to use it for when two lines intersect, any help with this would be much appreciated

Justin
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    Suppose you have two straight lines as: $f_1(x)=m_1x+c_1\ \ and\ \ f_2(x)=m_2x+c_2$. Now, finding the intersection of these two lines is same as finding the root of the equation $f_1(x)-f_2(x)=0$ – dibyendu Oct 23 '13 at 10:40
  • Assuming that the lines are straight and you have the equations for them, you wouldn't need the bisection method. Are the lines straight and do you have the equations for them? – George Tomlinson Oct 23 '13 at 10:57

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To determine where any two curves $y=f(x)$ and $y=g(x)$ intersect (and lines are considered 'curves' for this purpose), simply set $f(x)=g(x)$. The reason this works, is that you are looking for pairs $(x,y)$ that satisfy both equations simultaneously, so to ensure the $y$-coordinates are the same, implies that $f(x)=y=g(x)$. Now rewrite $f(x)=g(x)$ as $f(x)-g(x)=0$, and your question boils down to finding the root(s) of the function $f-g$.

Shaun Ault
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