A determining apparatus for determining whether a road surface is slippery or not as a state of the road surface on which a vehicle is traveling, comprising: a rotational velocity acquiring portion configured to sequentially acquire a rotational velocity of tires (T FL, T FR, T RL, T RR) fitted to the vehicle; a slip ratio calculating portion configured to sequentially calculate a slip ratio of the tires (T FL, T FR, T RL, T RR) based on the sequentially acquired rotational velocity; a driving force acquiring portion configured to sequentially acquire a driving force of the vehicle; a slope calculating portion configured to calculate a slope of the slip ratio relative to the driving force, as a regression coefficient indicating a linear relationship between the slip ratio and the driving force; and a determining portion configured to determine a state of the road surface based on the slope, wherein the determining portion determines that the road surface is slippery in the case in which the calculated slope is at least a threshold value, characterized in that the slope calculating portion calculates the slope, and calculates an intercept as another regression coefficient indicating the linear relationship, based on a large number of data sets of the slip ratio and the driving force at the time of determination of a state of the road surface and therebefore, in a case in which it is determined that a variation of the driving force is at least a certain value at the time of determination of a state of the road surface, and calculates the slope based on the data set of the slip ratio and the driving force at the time of determination of a state of the road surface, and the intercept that has been already obtained, in a case in which it is determined that the variation is less than the certain value at the time of determination of a state of the road surface. a rotational velocity acquiring portion configured to sequentially acquire a rotational velocity of tires (T FL, T FR, T RL, T RR) fitted to the vehicle; a slip ratio calculating portion configured to sequentially calculate a slip ratio of the tires (T FL, T FR, T RL, T RR) based on the sequentially acquired rotational velocity; a driving force acquiring portion configured to sequentially acquire a driving force of the vehicle; a slope calculating portion configured to calculate a slope of the slip ratio relative to the driving force, as a regression coefficient indicating a linear relationship between the slip ratio and the driving force; and a determining portion configured to determine a state of the road surface based on the slope, wherein the determining portion determines that the road surface is slippery in the case in which the calculated slope is at least a threshold value, characterized in that the slope calculating portion calculates the slope, and calculates an intercept as another regression coefficient indicating the linear relationship, based on a large number of data sets of the slip ratio and the driving force at the time of determination of a state of the road surface and therebefore, in a case in which it is determined that a variation of the driving force is at least a certain value at the time of determination of a state of the road surface, and calculates the slope based on the data set of the slip ratio and the driving force at the time of determination of a state of the road surface, and the intercept that has been already obtained, in a case in which it is determined that the variation is less than the certain value at the time of determination of a state of the road surface. calculates the slope, and calculates an intercept as another regression coefficient indicating the linear relationship, based on a large number of data sets of the slip ratio and the driving force at the time of determination of a state of the road surface and therebefore, in a case in which it is determined that a variation of the driving force is at least a certain value at the time of determination of a state of the road surface, and calculates the slope based on the data set of the slip ratio and the driving force at the time of determination of a state of the road surface, and the intercept that has been already obtained, in a case in which it is determined that the variation is less than the certain value at the time of determination of a state of the road surface.