Taking the reciprocal of both sides of the Michaelis-Menten equation yields the Lineweaver-Burk Equation:
$ \dfrac{1}{V} = \dfrac{K_m}{V_{max}}\dfrac{1}{[S]}+ \dfrac{1}{V_{max}} $
Plotting a $ \dfrac{1}{V}$ vs. $\dfrac{1}{[S]}$ graph, I am told that:
y-int $= \dfrac{1}{V_{max}}$ and
x-int $= -\dfrac{1}{K_m}$
How are these relationships derived from the lineweaver-burk plot? I can see how the y-intercept can be equal to $\dfrac{1}{V_{max}}$ if $\dfrac{1}{[S]} = 0$, but I don't see how x-int $= -\dfrac{1}{K_m}$ by setting $\dfrac{1}{V} = 0$? Can someone demonstrate how these relationships were derived?
y=mx+c
ory=m(x-d)
wherec
is y-intercept andd
is x-intercept. The general equation of a line isy-y₁=m(x-x₁)
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