For the Michaelis–Menten model plotted as a Lineweaver–Burk double-reciprocal graph, what is the slope of the line in terms of Km and Vmax?

Introduction / Context:
The Lineweaver–Burk plot linearizes the Michaelis–Menten equation to estimate kinetic parameters. Recognizing the slope and intercepts is essential for basic enzyme kinetics and for interpreting inhibition patterns in pharmacology and biotechnology.

Given Data / Assumptions:

• Michaelis–Menten kinetics applies.
• Plot is 1/v (y-axis) versus 1/[S] (x-axis).
• Km is Michaelis constant; Vmax is maximum velocity.

Concept / Approach:
Start from v = (Vmax * [S]) / (Km + [S]). Take reciprocals: 1/v = (Km/Vmax)(1/[S]) + (1/Vmax). This is in the form y = m x + b with slope m = Km/Vmax and y-intercept b = 1/Vmax.

Step-by-Step Solution:

Verification / Alternative check:
Graphically, increasing Km (weaker substrate affinity) at fixed Vmax steepens the line, consistent with higher Km/Vmax slope.

Why Other Options Are Wrong:

• Vmax/Km: Inverse of the slope.
• 1/Km and 1/Vmax: These correspond to intercepts in other reciprocal plots, not the LB slope.
• Km * Vmax: Not a slope in the LB framework.

Common Pitfalls:
Confusing x- and y-intercepts with slopes, or mixing up Eadie–Hofstee and Hanes–Woolf forms.

Final Answer:
Km/Vmax.