Step 1: A non-competitive inhibitor binds at a site different from the active site and can attach to either the free enzyme or the enzyme-substrate complex.
Step 2: Because it does not compete with substrate for the active site, raising substrate concentration cannot reverse the effect. This lowers the apparent Vmax.
Step 3: Since substrate binding itself is unaffected, the Km stays unchanged.
Step 4: On a Lineweaver-Burk plot, lines for inhibitor and no inhibitor cross on the x-axis (same Km, 1/Vmax intercept higher). So the correct statement is: Km remains same, Vmax decreases.
Ref: Lippincott's Illustrated Reviews, Biochemistry, 5th edn, pg 61.