Why does a steeper load line gives higher current gain, while a flatter line gives higher voltage gain? I read multiple tutorials where they only provide a graph without explanation and I can't visualize why it is.

For the upper load line, if a small or input signal fluctuates on a DC-biased base current (e.g. 40uA in the image) at a fixed operating voltage of \$V_{CE}\$, then the output amplified current, or \$I_C\$ fluctuates around 5mA. And for the lower load line, if small signal rides on the 20uA base current, output collector current fluctuates around 3mA with more of less the same amount. In either case, I don't see where \$ \partial I_c \over \partial I_b\$ differs for different load lines. Same question for the voltage gain.

Why does a steeper load line gives higher current gain, while a flatter line gives higher voltage gain? I read multiple tutorials where they only provide a graph without explanation and I can't visualize why it is.

For the upper load line, if a small or input signal fluctuates on a DC-biased base current (e.g. 40uA in the image) at a fixed operating voltage of \$V_{CE}\$, then the output amplified current, or \$I_C\$ fluctuates around 5mA. And for the lower load line, if small signal rides on the 20uA base current, output collector current fluctuates around 3mA with more of less the same amount. In either case, I don't see where \$ \partial I_c \over \partial I_b\$ differs for different load lines. Same question for the voltage gain. 

[EDIT]

Is that what it means by saying a steeper line gives higher current gain?