def METHOD_NAME(self):
    """Advance to the next point in the line."""
    if self.x1_ > self.x0_:
        if self.x_ < self.x1_:
            self.x_ = round(self.clamp(
                self.x_ + self.step_size_, self.x0_, self.x1_), 5)
            self.y_ = round(self.m_ * self.x_ + self.b_, 5)
        else:
            self.valid_ = False
    elif self.x1_ < self.x0_:
        if self.x_ > self.x1_:
            self.x_ = round(self.clamp(
                self.x_ - self.step_size_, self.x1_, self.x0_), 5)
            self.y_ = round(self.m_ * self.x_ + self.b_, 5)
        else:
            self.valid_ = False
    else:
        if self.y1_ > self.y0_:
            if self.y_ < self.y1_:
                self.y_ = round(self.clamp(
                    self.y_ + self.step_size_, self.y0_, self.y1_), 5)
            else:
                self.valid_ = False
        elif self.y1_ < self.y0_:
            if self.y_ > self.y1_:
                self.y_ = round(self.clamp(
                    self.y_ - self.step_size_, self.y1_, self.y0_), 5)
            else:
                self.valid_ = False
        else:
            self.valid_ = False