What is the equation of the line that passes through the points (3,1) and(4,2)?

Question

A. y=x-2
B. y=x+2
C. y=2x-1
D. y=2-x

Answer 1

m = (2 - 1) / (4 - 3) = 1 / 1 = 1
y - 2 = 1 (x - 4)
y = x - 4 + 2
y = x - 2
OPTION A

Answer 2

a million)Equation a million and a couple of are the comparable (equivalent!) the two equation #a million and equation #2 characterize the line that passes by using the two given factors. 2) x = 4 3) x-intercept = (2, 0); y-intercept = (0, -6) 4) y + a million = 5(x + 2) 5) a million 6) something incorrect 7) y = -3/2x 8) something incorrect 9) 23 adults and 0 young ones

Answer 3

Please don't use this to do your homework. Try to understand the question.
the line will be of the form y=mx+b.
m(the slope)=the change in y over the change in x
in this case the change in y=1 and the change in x=1
so 1/1=1=m. Next solve for b. Use either the first or second point to get 1=(1)3+b or 2=(1)4+b
1=3+b 2=4+b
-2=b
so your final equation is y=x-2

Answer 4

A) y=x-2

when x is 3 (-2=1)
when x is 4 (-2=2)

Answer 5

Before demonstrating why such questions have nothing to do with proper testing of mathematical ability, let me first tell you that "A" is the only possible answer to this multiple-guess question.

Ordinarily, I'd compute the slope (which is m=1) and then compute the intercept "b", to get the equation: y = mx + b. That's fairly easy, and it might even constitute a reasonable math problem.
[SEE BELOW for a solution the hidden math problem, which your math teacher was too lazy to test.]

However, this is NOT a question about mathematics!
Instead, it is a "multiple-choice" question, and therefore does NOT measure any meaningful mathematical ability. [cf. Banesh Hoffman, "The Tyranny of Testing"]

Since the stupid question-writer not only gave you ALL FOUR POSSIBLE VALUES of X and Y but then limited your answers to only those choices, you can fake this lazy teacher out by just PLUGGING IN the given X and Y to those stupid choices and eliminate any that fail. In this case, three of them fail -- with only one of the X and Y value pairs!!! -- and only one of the dumb ABCD choces survives! It takes no mathematical ability to choose the only remaining choice, when all other choices have been eliminated in advance by the so-called "teacher".

Plugging in (3,1) or x=3 and y=1, gives the following choices:
A. y=x-2 = 1 = 3-2 .......... TRUE
B. y=x+2 = 1 = 3+2 ......... FALSE: 1 <> 5
C. y=2x-1 = 1 = 2(3) - 1 ... FALSE: 1 <> 5
D. y=2-x = 1 = 2 - 3 ........ FALSE: 1 <> -1
Obviously, the first one is true and all of the others are false.
Therefore, the answer is "A".
(Notice that this approach ALWAYS gets a correct answer, without doing any algebra; just a little bit of mathematics.)

The other choices were so badly chosen that it is not even necessary to test them with the second coordinate point, but if you want to waste your time plugging in (4,2), those choices become:
A. y=x-2 = 2 = 4-2 .......... TRUE
B. y=x+2 = 2 = 4+2 ......... FALSE: 2 <> 6)
C. y=2x-1 = 2 = 2(4) - 1 .... FALSE: 2 <> 8-1
D. y=2-x = 2 = 2 - 4 ........ FALSE 2 <> -2
However, that is entirely unnecessary!
(Since it is one of those silly "multiple-choice" questions, eliminating any choice one way eliminates it for all.)
Wow! You could have just as easily plugged in the second pair (4,2) and not bothered with (3,1).

Now, that is no way to test math!!!!!!
[Whaddaya expect form a noncompetitive government-school, with a teacher who is required to join a "union" to keep his job and whose tenure and salary is based upon "seniority" -- and therefore not affected by such things as actual student learning??? ]

Since multiple-guess questions MUST provide the correct answers, along with a few other choices which MUST be wrong, this establishes a quantized boundary conditions and thereby makes it EASIER to get the correct answer without actually doing the mathematics that the question was purportedly designed to test!!!!
All that is necessary for this sort of question is to eliminate the WRONG choices, and pick the one that is left. With multiple-guess questions, it is often possible to eliminate all but one choice by various methods (such as eliminating plausible-but-obvious answers that would not pass "validation" processes.)


P.S. The question you were given was faulty and worthless, BECAUSE it offered multiple choices. A much more meaningful (and FAIR) question might be composed from the same information, without giving the stupid choices (THREE of which were guaranteed to be wrong, and one correct.)

As a far better measure of mathematical ability, you might have been expected to notice that the two points on the line have a rise of 1 (2-1) for a run of 1 (4-1), so the slope is 1.
That eliminates choices C and D (which have slopes of 2.) Then, you would have to sect between them based on the intercept.
However, for stupid multiple-choice questions like this, it is simpler to just plug in the given (X,Y) points.

By the way, that worthless "SAT" exam (which, sadly, still governs college acceptance) also uses stupid multiple-choice math questions like this -- which makes it VERY easy for mediocre math students to learn how to score high on that phony exam, regardless of their mathematical ability.

P.P.S. To be fair, I would like to give credit and deserved attribution to a source from which I have recently learned many of the above things. A few decades ago, John Katzman recognized the unfair nature of the SAT and other multiple-guess tests, analyzed their characteristics. He then started a company named "The Princeton Review" (TPR), which trains students avoid the unfair traps inherent in multiple-guess "testing". I am indebted to Katzman (whom I have never met) for some of my recent insights into the way in which these tests are utterly bogus, and also for several very-effective techniques to beat them. (My undergrad degree was in Mathematics, but TPR has taught me many valuable things that I never learned in school!)

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Answer 6

y = mx + c

m = (2-1)/ (4 - 3)
= 1/1
= 1

(1) = 1 (3) + c
c = -2

Ans: y = x -2
Ans is (a)

Answer 7

2 and a half cuts right down the middle

Answer 8

I got y=x+1 oh well sorry kid wait i think i got it hold on

1.) find the slop; slope (or m) = (y2-y1)/(x2-x1)
= (2-1)/(4-3)
= 1
2.) Plug in the equation
y-y1=m(x-x1)
y-(1)=1(x-3)
y= x-2
so It's A!!!!!!

Answer 9

graph it

i think it goes like this

A. go down 2 spaces on x-axis, then up one and to the right one

B. go up 2, then up one right one

C. down 1, then up 2 right 1

D. go down up 2 then up 1 and to the LEFT one

Answer 10

Its Definately A!