A novel three-dimensional simultaneous B1 and T1 mapping method is introduced: the method of slopes (MoS). The linearity of the spoiled gradient recalled echo (SPGR) signal vs flip angle relation is exploited: B1 mapping is achieved by a two-point extrapolation to signal null with a correction scheme while T1 mapping uses the slopes of the SPGR signal vs flip angle curves near the origin and near the signal null. This new method improves upon the existing variable flip angle (VFA) T1-mapping method in that (i) consistency between B1 and T1 maps is ensured (ii) the sampling scheme is T1-independent (iii) the noise bias and singularity, associated with using a linear form for the SPGR signal equation, is eliminated by using the full equation. The method is shown to yield accurate and robust results via simulations. Initial estimates of B1 and T1 values are obtained from three data points via simple computations and straight line approximations. Initial estimates of B1 values, for a range of values, are shown to be accurate due to the proposed B1 correction scheme. The accuracy and robustness of T1 values is achieved via a non-linear fitting algorithm which includes a fourth data point sampled at high SNR. The MoS was validated by comparing resulting B1 and T1 maps with those obtained using other standard methods. Finally, the ability to obtain brain B1 and T1 maps using the MoS was demonstrated by in vivo experiments. The MoS is expected to perform well on other motion-free anatomical regions as well. Copyright © 2012 John Wiley & Sons, Ltd.