Introduction

In enzyme kinetics, graphical methods are used to determine important constants
like V_max and K_m. The
Lineweaver–Burk plot, also known as the double reciprocal plot,
converts the curved Michaelis–Menten graph into a straight line for easier calculation of
kinetic parameters.

Step 1: Michaelis–Menten Equation

v₀ = (V_max[S]) / (K_m + [S])

Where:
v₀ = initial velocity
V_max = maximum velocity
K_m = Michaelis constant
[S] = substrate concentration

Step 2: Take Reciprocal

1/v₀ = (K_m + [S]) / (V_max[S])

Step 3: Rearranging

1/v₀ = (K_m/V_max) × (1/[S]) + 1/V_max

Step 4: Compare with Straight Line Equation

y = mx + c

• y → 1/v₀
• x → 1/[S]
• Slope → K_m/V_max
• Intercept → 1/V_max

Therefore, Lineweaver–Burk plot is 1/v₀ vs 1/[S].

Explanation of Each Option

(A) 1/v₀ vs 1/[S]
Produces a straight line and helps calculate kinetic parameters → Correct

(B) v₀ vs [S]
Hyperbolic Michaelis–Menten curve, not linear → Incorrect

(C) v₀ vs 1/[S]
Does not give linear relationship → Incorrect

(D) 1/v₀ vs [S]
Not derived from the equation → Incorrect

Graph Properties

• Y-axis → 1/v₀
• X-axis → 1/[S]
• Straight line obtained
• Slope → K_m/V_max
• Y-intercept → 1/V_max
• X-intercept → −1/K_m

Final Answer

(A) 1/v₀ vs 1/[S]

Quick Exam Shortcut

Remember: Lineweaver–Burk = Double Reciprocal Plot
So both axes contain reciprocals.

Key Takeaways

• Linear form of Michaelis–Menten equation
• Helps determine V_max and K_m
• Straight-line graph
• Always reciprocal vs reciprocal