1. INTRODUCTION
2. DATA, SAMPLE, AND MEASUREMENTS
2.1. MOSDEF Survey
2.2. Slit Loss Corrections and Line Flux Measurements
2.3. Sample Selection
2.4. Stellar Population Modeling
2.5. Hα SFRs
2.6. Excitation-sensitive Line Ratios, Gas-phase Metallicities, and ξ ion
2.7. Equivalent Width (W) Measurements
3. RELATIONS
3.1. Stellar Mass
3.2. UV Slope
3.3. Age
3.4. SFR and sSFR
3.5. Excitation and Gas-phase Metallicity
3.6. Ionizing Photon Production Efficiency (ξ ion)
4. DISCUSSION
4.1. The Sensitivity of [O III] Equivalent Width to Mass, Metallicity, and SFR
4.2. Trends for Emission Lines Other Than [O III]
4.3. Other Redshift-dependent Trends 
4.4. Equivalent Width versus Excitation Conditions
4.5. Redshift Invariant Trends with sSFR and Age
4.6. Redshift Evolution of Equivalent Widths
4.7. A Strategy for Identifying High-excitation and High-ionization Galaxies
5. CONCLUSIONS