A linearly slotted waveguide antenna (LSWA) is investigated. The slot is placed in one of the narrow faces of a rectangular waveguide, which operates at Ka-band (26.5-40 GHz), which is in a frequency range including upper microwaves and the lower edge of millimeter waves. Analytically, the magnetic current approach is applied. Some antenna parameters of this structure are experimentally measured and it is observed that the antenna radiates a single transversal-polarized beam that scans with frequency. The experimentally obtained patterns in 2 perpendicular planes are also correlated with analytical and numerical patterns that use the magnetic current model and HFSS, respectively. Approximate maximum directivity and side lobe level of the antenna are 20 dBi and -10 dB, respectively. In a frequency range of 23-35 GHz, efficiency above 75% is obtained by this investigated antenna. Travelling wave parameters of the antenna are also calculated. The antenna is a fast-wave structure and exhibits frequency-scanning behavior with an average scanning rate of 2.14 degrees /GHz. Some of the results of the investigated LSWA are also compared with the results of the sinusoidal slotted waveguide antenna (SSWA) investigated in a previous study by the author. The directivity and efficiency of the linear slot is better than that of the sinusoidal slot, while the other characteristics are similar. Thus, the LSWA exhibits a better performance than the SSWA does if we consider the transversal E-phi polarization (SSWA has another polarization as well, which is longitudinal E-0 polarization). It is also concluded that this frequency-scanning Ka-band LSWA can be used in telecommunications and radar applications.