Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 30

Determine an equation for the line that goes through $(2,-5)$ and $(1,4)$

a.) Write the equation in slope intercept form.
b.) Write the equation in standard form

We are given $(x_1, y_1) = (2, -5)$ and $(x_2, y_2) = (1,4)$
a.) Then by using two point form, we have

$
\begin{equation}
\begin{aligned}
y - y_1 &= \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)\\
\\
y -(-5) &= \frac{4 - (-5)}{1 - 2} (x - 2)\\
\\
y + 5 &= \frac{4 + 5 }{1 - 2} (x - 2)\\
\\
y + 5 &= \frac{9}{-1}(x -2)\\
\\
y + 5 &= -9x + 18
\end{aligned}
\end{equation}
$

So, the equation in slope intercept form is
$y = -9x + 13$

b.) Thus, the equation in general form $Ax + By = C$, we get
$9x + y = 13$

Why does Krebs want a close relationship with the girls he watches?

Krebs comes back to his hometown later than the other soldiers. He comes back after the townspeople have had enough of the war stories told by the soldiers come back home. He comes back after the furor over the homecoming of the war heroes has died down. The townspeople have heard so many stories told of the “atrocities of the war” that they are not enthralled by Krebs’s stories. He comes back to Oklahoma to find that all the young girls have grown up and are almost strangers to him as they have what the text describes as “well-defined alliances and shifting feuds” that he finds too exhausting to penetrate. However, he likes to watch them because they look really beautiful. He also loves their attires, the “round Dutch collars above their sweaters, their silk stockings and flat shoes.”
Krebs wishes that he could develop a close relationship with the girls he watches, because he finds them attractive. However, he does not want to work hard at getting girls. He is not keen on the courting process and views it as a tedious activity. It seems that Krebs has commitment issues and prefers women who are not conversationalists. The fact that he says that he does not want to shoulder the consequences that come with romantic relationships "again” and that he is uninterested in going through the complications of developing a romantic relationship in his hometown “again” hints at a past painful relationship that he might have had sometime before the war.

From chapters 22 and 23 of To Kill a Mockingbird, what literary techniques are used?

Literary techniques, sometimes called narrative techniques, encompass many different strategies that authors use to tell a story. Some examples of literary techniques include juxtaposition, the use of foils, flashbacks, plot twists, and foreshadowing. Chapters 22 and 23 detail events that take place after the Tom Robinson trial. Jem, specifically, struggles through the painful effects of a bildungsroman--otherwise known as a coming-of-age story. For example, Lee tracks Jem's steps from the courtroom to Miss Maudie's house, then to having discussions with Atticus about what occurred during the trial. Jem is baffled that Tom was not allowed to go free. He describes his disappointment with a simile as follows:

"It's like being' a caterpillar in a cocoon, that's what it is . . . Like somethin' asleep wrapped up in a warm place. I always thought Maycomb folks were the best folks in the world, least that's what they seemed like" (215).

Jem's disenchantment with the people of his town opens up the way for him to realize the realities of life in the South. What seemed like a good life in Maycomb is now destroyed by Jem's experience with the prejudices shown during the trial of Tom Robinson. Jem's naive hope that the world always seeks what's right, or that truth will always prevail, is destroyed. As a result, a boy faces the realities of the adult world and must come to terms with them. Consequently, he will never be able to return to his child-like, naive self. 
In chapter 23, discussions at the Finch house become more serious in nature. Jem's brain is filled with questions as he seeks answers while going through his rite of passage. Jem doesn't understand why Tom Robinson would get the death penalty for a conviction of rape. This leads Atticus to teach his son that the problem lies with the prejudices against African Americans, not the law. Atticus gives Jem a lesson on the following clarifying truth:

"As you grow older, you'll see white men cheat black men every day of your life, but let me tell you something and don't you forget it--whenever a white man does that to a black man, no matter who he is, how rich he is, or how fine a family he comes from, that white man is trash" (220).

Thus, Atticus teaches his son about the realities of the adult world in the South. Jem must face these facts and make a decision about what type of man he will become. Therefore, the primary technique used in chapters 22 and 23 is a bildungsroman because the focus is on explaining to Jem about what actually happened during the Tom Robinson trial. Once Jem accepts these new realities, he will enter the world of adults.  
One other technique used in chapter 23 has to do with creating foil characters with Atticus Finch and Bob Ewell. Foils are two characters who are complete opposites of each other. They are pitted against each other to show the difference between two different thoughts, philosophies, or agendas. For example, Atticus represents everything good, wholesome, proper and fair. On the other hand, Bob Ewell is disgusting, uneducated, ill-mannered, and a liar. When Bob Ewell challenges Atticus to a fight, he is disappointed that Atticus's response is that he's too old to fight. As a result, Atticus comes off looking like the better man on so many levels. Not only is Atticus kind and compassionate, but he doesn't hold a grudge towards one of the meanest men in Maycomb, either. For instance, Atticus tells Jem the following about Bob Ewell:

"Jem, see if you can stand in Bob Ewell's shoes a minute. I destroyed his last shred of credibility at that trial, if he had any to begin with. The man had to have some kind of comeback, his kind always does. So if spitting in my face and threatening me saved Mayella Ewell one extra beating, that's something I'll gladly take" (218).

Not only does Bob Ewell spit in Atticus's face, but he also calls him derogatory names in public. Atticus doesn't respond because he can't be provoked to lower himself to Ewell's level. By pitting an evil man against one of the kindest, most loving, and self-contained characters, Lee creates an excellent example of the use of foils to drive her plot forward. The discussions about Bob Ewell in the Finch home after the threatening public display center around protecting themselves from future attacks. These family discussions, and subsequent worries about Ewell by the children, foreshadow the attack on Jem and Scout later on in chapter 28. The following exchange between Atticus and Alexandra can be viewed as a foreshadowing:

"We don't have anything to fear from Bob Ewell, he got it all out of his system that morning.'"
"'I wouldn't be so sure of that, Atticus,' [Aunt Alexandra] said. 'His kind'd do anything to pay off a grudge. You know how those people are'" (218).

Aunt Alexandra's words ring true in the end; therefore, this is a foreshadowing of things to come from this point in the story.

How do I write a compound sentence?

A compound sentence is when two independent clauses are joined together and connected with a comma and a conjunction.
An independent clause is one that expresses a complete thought. It is called independent because it should be able to stand alone as a complete thought. It must have a noun and a predicate (subject). For example: Paul ran down the street.
The clauses are connected with a conjunction. A way to remember the options for conjunctions is the mnemonic device FANBOYS. Fanboys stands for: for, and, nor, but, or, yet, so. The job of the conjunction is to connect the two independent clauses. The comma comes before the conjunction
Example:
independent clauses:
Paul ran down the street.
He fell off his bike.
Compound sentence:
Paul ran down the street, and he fell off his bike.
As you can see, the two parts of the sentence are independent and can stand alone, but they are connected with a comma and a conjunction.

A simple sentence is an independent structure that has a subject and a verb , and it expresses a complete idea. When you have 2 independent clauses ,you can put them together and create a compound sentence. To do so, you will need to use linking words, also known as coordinating conjunctions. These are: for, and, nor, but, or, yet and so. (You can use the word FANBOYS as a way to remember their initials and bring them to your mind quickly)
Each of these words will indicate the relationship between the 2 ideas you are linking.
for: reason
and: addition
nor: disjunction
but: contrast
or: alternative
yet:concession
so: result
Do not forget there must be a subject and a verb in each part of the sentence ( each clause) for it to be a compound sentence! Also take into account we write a comma before the linking word.
examples: Mary did the cooking, and her husband did the washing.
The show is interesting, but the tickets are too expensive.
You can pick up the parcel at the office, or they can send it to you .

Compound sentences simply involve putting together (or "compounding") two sentences with a comma and a joining word (or "coordinating conjunction"). Coordinating conjunctions include and, but, or, for, nor, yet, and so. One of the key parts of understanding compound sentences is knowing that the pieces must be able to stand on their own as independent clauses.
Be careful: Just because you see a comma and a coordinating conjunction doesn't mean the sentence is a compound sentence. For example, "Simon is playing Pokemon, and having a lot of fun" is not a compound sentence. Why not? Because "having a lot of fun" is not an independent clause, and the comma technically shouldn't be there (though very casual writers sometimes add one). The correct version of this as a compound sentence would be:

Simon is playing Pokemon, and he is having a lot of fun. 

Let's consider some other examples of compound sentences:

Alice wants to get ice cream at Dairy Queen, but she is lactose intolerant. 
Gordon is busy with work, so I went to dinner with Victoria instead.
We will go see Batman v. Superman tonight, or we will stay at home and watch Netflix.

In Silas Marner by George Eliot, what does Silas come to love in Raveloe apart from his work?

Arguably, Silas loved many things throughout his years in Raveloe. It really depends on what he was focusing on at the moment. However, it is arguable that Eppie is the source of love in Silas's life.
At first, Silas's love was the pleasure of being alone with the loom, working very hard, trying to focus on ending the grief in his life. Then, it was the money and gold that he acquired from all this extra work. He became quite fixated with it, and even vowed his dedication to it. It was because of his unhealthy love for his gold that, when it was stolen, Silas lost his mind and ended up at the Rainbow Inn, suffering a total nervous breakdown.
This is the time when Eppie shows up in his life, and warms his heart forever. Along with it, the people from Raveloe gave Silas all the care and support that, eventually, changed him for good. Still, the love Silas developed for his adoptive daughter definitely would rival any love he ever felt before or after, as his words to Godfrey clearly state when the latter tries to claim his biological daughter back:

"Then, sir, why didn't you say so sixteen years ago, and claim her before I'd come to love her, i'stead o' coming to take her from me now, when you might as well take the heart out o' my body? God gave her to me because you turned your back upon her, and He looks upon her as mine: you've no right to her!

Therefore, Eppie is the greatest love that Silas would ever have in life.

What are some texts related to Steinbeck's Of Mice and Men?

One text related to Of Mice and Men would be Steinbeck's The Grapes of Wrath.  It expands many of the ideas in Of Mice and Men.  The Joad family is similar to George and Lennie.  In both, we see protagonists who have to struggle to realize their dreams.  Both works are very similar in their depiction of people who fight against the crushing reality of poverty.  The antagonists in both works use money and influence as a way to crowd out others.  In addition to this, "sage-like" figures in both works help to provide a moral compass in a world that lacks it.  Slim is very similar to Jim Casy. Finally, both works are similar in that they are sad, but ultimately affirm the power of restoration in a world of condemnation. While The Grapes of Wrath  is considerably longer than Of Mice and Men, it would be a good complement to it because it underscores many of the same themes.
A different, but related read is Tillie Olsen's "I Stand Here Ironing."  This story is about a mother's recollections in raising her daughter during the 1930s.  The Great Depression is a shared setting in both Olsen's work and Steinbeck's novella.  Both works have very distinct approaches to how poverty impacts emotional connection.  One could almost envision a conversation between George and the mother in Olsen's story as they both live in a world where poverty impacts emotions.  Both of them had to take care of someone who required so much more than they could give.  Olsen's and Steinbeck's works both discuss how economic poverty impacts emotional poverty. 
Finally, I'll offer a very different suggestion for the last one.  One of the major themes in Of Mice and Men is how dreams influence individual identity.  Dreams are a significant part of the story.  Everyone has them, from George's and Lennie's shared dream, to Candy joining them, to Crooks, who wishes for a moment to be a part of something.  Even Curley's wife yearns for her dreams of being in "pitchers."  It might be fascinating to contrast the dreams of these people who are poor with the vision of dreams offered in F. Scott Fitzgerald's The Great Gatsby.  While the world of Jay Gatsby is completely different than the "bindle stiff" existence, it is interesting to examine the role that dreams play in both works.  In the end, George and Lennie are unable to accomplish their dream.  Yet, so is Gatsby.  In both settings, the failure of dreams cut across socio-economic lines.  It might be powerful to see how broken dreams can be appreciated by both rich and poor.  Social class cannot prevent the hurt of our failed dreams.

What were the failures of Aristotle?

Aristotle is widely considered on of the great thinkers in the history of western civilization. He wrote about everything from ethics to biology and metaphysics to astronomy. His works have been seminal in terms of how subsequent thinkers have approached topics as diverse as classification of plants, analysis of literature, teaching public speaking, and formal logic. Although we have advanced considerably in many of these fields over the past two millennia, it isn't necessary to characterize elements of his work which have been superseded as "failures"; it might be better to think of them as pioneering efforts. Newton, whose theory of gravitation superseded Aristotle's belief in the natural motions of elements, acknowledges this when he says, "If I have seen further it is only by standing on the shoulders of giants."
In general, Aristotle's works in the sciences are among those most likely to have been proven wrong with advances in technology. His ideas concerning physics, astronomy, and biology are obsolete. In literary theory, his Poetics, although still influential, is limited by its focus on only a limited number of works of one particular culture, and especially by his ignorance of prose fiction. In ethics, his concept of "natural slavery" is one many of us would find repugnant, as we would his assumptions about gender. One could also say that his ethical and political ideas are limited by a viewpoint that accepts human inequality and the power of elites as natural phenomena. He was also, like most Greeks, rather insular, tending to despise other cultures as "barbaric" rather than exploring cultural differences objectively.