He was the first black to be elected as president. 

他是第一位被选为总统的黑人。(不定式短语 to be elected as president 与谓语动词 was 同时发生，与所修饰的 the first black 是动宾关系)

to be elected修饰中心名词“the first black”与中心名词存在逻辑上被动主谓关系。即相当于“The first black was elected as a president”

(被修饰名词the first black是不定式逻辑宾语，即动词不定式动作承受者。）

不定式(to do/to be done)作后置定语修饰“中心名词”

(A)中心名词+to do的结构中，名词与不定式存在以下几种理解

(1)中心名词为不定式逻辑主语，与不定式存在逻辑上主动主谓关系。

He is the person to help you with your English.

He is the first person to arrive here.

Tom is the best person to do the work.

She was always the first to come and the last to leave

(2)中心名词为不定式逻辑宾语，与不定式存在逻辑上动宾关系。

He has so much work to do.

She has some clothes to wash.

I have some letters to write.

(B)中心名词+to be done 名词与不定式存在以下理解

中心名词为不定式逻辑宾语，与不定式存在逻辑上被动主谓关系。

The next thing to be done is to carry away the earth.

She is only the person to be invited to attend the meeting.

除了不定式to do与被修饰名词/代词以上主谓关系和动宾关系，还存在以下几种关系。

(1)同位关系

We made a plan to learn from Lei Feng.

His decision to go to America surprised his parents.

(2)动状关系

He has no time to go there.

That is the way to do it.