In an Eadie-Hofstee plot, which relationship holds between slope and intercept?

In an Eadie-Hofstee plot, which relationship holds between slope and intercept?

• A. The slope equals -Km and the intercept equals Vmax
• B. The slope equals -Vmax and the intercept equals Km
• C. The slope equals Km and the intercept equals Vmax
• D. The slope equals -Km and the intercept equals -Vmax

Answer: (A)

The key idea is the linear form of the Michaelis–Menten equation when you plot v versus v/[S]. Starting from v = (Vmax[S])/(Km + [S]), rearranging gives v = -Km · (v/[S]) + Vmax. This shows the line has a slope of -Km and a y-intercept of Vmax. Physically, the intercept Vmax is the maximal rate at saturating substrate, and the slope magnitude equals Km, reflecting the substrate affinity. So the correct relation is that the slope is negative Km and the intercept on the v-axis is Vmax. The other options assign incorrect signs or swap Km and Vmax, which don’t follow from the transformation.

The key idea is the linear form of the Michaelis–Menten equation when you plot v versus v/[S]. Starting from v = (Vmax[S])/(Km + [S]), rearranging gives v = -Km · (v/[S]) + Vmax. This shows the line has a slope of -Km and a y-intercept of Vmax. Physically, the intercept Vmax is the maximal rate at saturating substrate, and the slope magnitude equals Km, reflecting the substrate affinity.

So the correct relation is that the slope is negative Km and the intercept on the v-axis is Vmax. The other options assign incorrect signs or swap Km and Vmax, which don’t follow from the transformation.