Lineweaver-Burk

5 min read Updated Apr 18, 2026

Hyperbolas are annoying to analyze. Straight lines are easy. The Lineweaver-Burk plot linearizes the Michaelis-Menten equation by taking the reciprocal of both sides, which makes it easy to read Km and Vmax off a graph and diagnose inhibitor types at a glance.

The Linearization

Start with Michaelis-Menten.

$V_0 = \frac{V_{max}[S]}{K_m + [S]}$

Flip both sides.

$\frac{1}{V_0} = \frac{K_m + [S]}{V_{max}[S]} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

That is the equation of a line when 1/V0 is plotted against 1/[S].

What to Read Off the Plot

Lineweaver-Burk double reciprocal plot showing 1/V0 on the y-axis and 1/[S] on the x-axis. The y-intercept is 1/Vmax, the x-intercept is -1/Km, and the slope is Km/Vmax — Lineweaver-Burk plot. The y-intercept gives 1/Vmax. The x-intercept gives -1/Km. The slope is Km/Vmax. *Credit: Wikimedia Commons, public domain*

Feature	Meaning
y-intercept	1 / Vmax (so a higher y-intercept means a lower Vmax)
x-intercept	-1 / Km (so a more negative x-intercept, farther from origin, means a smaller Km and higher affinity)
Slope	Km / Vmax

Why the Plot Matters for Inhibitors

The real power of Lineweaver-Burk is distinguishing inhibitor types by how the lines shift.

Inhibitor type	What moves	Intuition
Competitive	x-intercept moves right (Km up), y-intercept unchanged (Vmax unchanged)	More substrate needed to win the competition, but top speed is still possible
Noncompetitive	y-intercept moves up (Vmax down), x-intercept unchanged (Km unchanged)	Broken enzyme molecules cannot go faster; remaining ones still bind normally
Uncompetitive	Both intercepts shift toward origin. Lines are parallel (same slope). Vmax and Km both decrease	Inhibitor traps ES complex, so effective affinity increases but top speed falls
Mixed	Both intercepts move. Slope changes. Vmax always drops; Km may rise or fall	Hybrid case - inhibitor binds both E and ES but with different affinities

We will unpack each of these in the next three sections. For now, memorize what to look for on the plot.

Common Trap: Direction of Change

A “higher” y-intercept on Lineweaver-Burk means a LOWER Vmax (because the y-intercept is 1/Vmax). A “more positive” x-intercept - closer to zero or right of it - means a HIGHER Km. Students constantly flip this sign. Practice with a dozen plots until it is automatic.

Worked Example: Reading Km and Vmax from a Plot

A passage hands you a Lineweaver-Burk plot with a y-intercept at 0.02 (min/µM) and an x-intercept at -0.1 (1/µM). Find Km and Vmax.

On a Lineweaver-Burk plot, where is Vmax read off and where is Km read off?

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Vmax is read off the y-intercept (y-intercept = 1/Vmax). Km is read off the x-intercept (x-intercept = -1/Km). A larger y-intercept value means smaller Vmax. A less negative x-intercept means larger Km.

Two Lineweaver-Burk lines cross exactly on the y-axis when an inhibitor is added. What type of inhibitor is it?

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Competitive. If the y-intercept is unchanged, Vmax is unchanged. The x-intercept shifts (Km rises), but at infinite substrate, the enzyme can still hit the same top speed. That is the signature of competitive inhibition.

The Lineweaver-Burk plot shows parallel lines before and after adding an inhibitor. What type is it?

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Uncompetitive. Parallel lines mean the slope (Km/Vmax) is unchanged, but both intercepts shift. Both Vmax and Km decrease by the same factor, so their ratio stays constant.