Question

True of False
1.The equation of every line can be written in point-slope form.

2. If two nonvertical lines are parallel, they have the same slope

3.If the x and y intercepts of a line ar erational and nonzero, then the slope of the line is rational

4.(3x-2y+4)+m(2x+6y-2) = 0 is the equation of a line for each real number m.

5.The natural domain of T(theta) = sec(theta) + cos(theta)

6.The range of the function f(x) = tanx - secx is the set (-inf,-1]U[1,inf).

Answer 1

Well what do you think?

Answer 2

Please provide counter examples to all those things you consider false.

Answer 3

1. I believe it is true.
2. True, since that is what makes them parallel
3.Honestly I just don't understand the question there. I would suppose it is rational?
4.Again, don't really see what it is saying.
5.Looking at the graph I want to say True.
6.Looking at the graph, I think false.

Answer 4

Nice Try. Consider a vertical line and try #1 again.

Answer 5

What has the intercept to do with the slope? Nothing! Forget #3 FALSE.

Answer 6

so y = x. I guess that wouldn't be in that form.

Answer 7

No, y = x is in Slope-Intercept Form.

x = 2 is not, and cannot be in Slope-Intercept form.

Answer 8

@tkhunny are you saying all lines cannot be written in point-slope format?

Answer 9

When did I say that? I said no VERTICAL line can be written in Slope-Intercept from.

Answer 10

#1 is false due to the fact that for vertical lines, slope is undefined.

Answer 11

I think I got 1-3 down..still stumped on 4-6..

Answer 12

#4 just wants to know if there is a value for 'm' that will make that expression NOT an equation of a line.

(3x-2y+4)+m(2x+6y-2) = 0

Let's try Slope-Intercept Form. It will be fun.

(3x-2y+4)+m(2x+6y-2) = 0

3x + 2mx - 2y + 6my + 4 - 2m = 0

6my - 2y = -3x - 2mx - 4 + 2m

y(6m-2) = x(-3-2m) + (2m-4)

y = x(-3-2m)/(6m-2) + (2m-4)/(6m-2)

Wasn't that as fun as I said?

The question is almost, is "Can 6m-2 = 0"? That would be no good. But would that just be a vertical line?

Answer 13

what was your answer for 3?

Answer 14

What's \(T(\theta)\)?

Answer 15

For #6, you may wish to convert to sine and cosine and get a different look at it.

Answer 16

That's all it says. The natural domain of T(Theta) = sec(theta) + cos(theta) is (-inf,inf)

Answer 17

For number 3 I have false.

Answer 18

For #3 it is false most of the times but there may be exceptions. If the y-intercept is \(\sqrt{32}\) and the x-intercept is \(\sqrt{2}\), couldn't the slope be rational?

Answer 19

For #5, the domain for T is same as the domain for the secant function.

Answer 20

#3 We only get TRUE or FALSE. There is no CONDITIONAL. It may be that it is so, but there is no inherent relationship. It is FALSE.

#5, I see. A "Natural Domain" is the Domain that has no arbitrary restriction.

\(T(\theta) = \sec(\theta) + \cos(theta) = \dfrac{1}{\cos(\theta)} + \cos(\theta)\)

It does appear that we are missing some things. What happens when \(\cos(\theta) = 0\)?

Answer 21

I think I'll stick with false for it. I mean, I'm not getting confirmation either way, but I think it is false as well.

Answer 22

Plotting #6 shows the range as \((-\infty, \infty)\).

Answer 23

So that one would be false? I'm getting really frustrated at these since I try working them and the homework thing gives me a wrong answer and doesn't specify which is wrong. Feel like I'm just feeling around in the dark here.

Answer 24

So far, the ones I feel like I KNOW are right are 1.F, 2.T, 3.F,6.F

Answer 25

Try 5F and 4T (there are exceptions to 4 but it is mostly true).

Answer 26

No dice.

Answer 27

How many tries are you allowed? Try 5F and 4F.

Answer 28

Unlimited. I've already attempted 40 =P

Answer 29

Still nothing D: . Feels like I've tried every combination up to this point, haha.

Answer 30

Just for fun try 3F.

Answer 31

That is 3F, 4F, 5F.

Answer 32

I already had 3 as F I think. but still, no go.

Answer 33

There are only 64 possibilities for all 6 questions. But a few of the questions are unambiguous and their answers can be fixed. And for every answer that is known for sure, the number possibilities will be lowered by a factor of 2.

Answer 34

gtg.

Answer 35

Holy crap I figured it! I just started messing around and got it.

Answer 36

1.F
2.T
3.T
4.T
5.F
6.F

Answer 37

Thanks for sticking around as long as you did!

Answer 38

You are welcome. Nice of you to post the final answers although 3 is a bit controversial. I gave an example of an exception earlier that would make it true but there are many for which it is false.