Questions About How To Find Slope

Betty asks…

How do you find slope intercept form for this line?

I need to find slope intercept form for a line passing through the point (5,8) and perpendicular to the line passing through the points (-8,7) and (-2,0).
Do you find the slope of the line passing through (-8,7) and then flip the slope?

admin answers:

Step 1: Find the slope of the perpendicular line passing thru (-8,7) (-2,0). Use point-slope formula:

m = (y1 - y2) / (x1 - x2)

. . = (7 - 0) / (-8 - (-2))

. . = 7 / (-8 + 2)

. . = 7 / - 6


Step 2: Get the slope of the line passing thru (5, 8) by flipping the above slope, and multiply by -1.

M = (- 6 / 7) * -1

. . = 6 / 7


Step 3: Use the point slope formula again to get the slope intercept form equation. Plug in what you know. Then solve for y.

M = (y1 - y2) / (x1 - x2)

6 / 7 = (8 - y)(5 - x)


Cross multiply

6(5 - x) = 7(8 - y)

30 - 6x = 56 - 7y

- 6x = 26 - 7y

- 6x + 7y = 26

7y = 26 + 6x

y = 26/7 + 6/7 x


Rearrange to get

y = 6/7 x + 26/7

Carol asks…

How to find function domains, and help finding slope of aline?

I'm having trouble finding the domain of functions. Could someone kindly explain how to get the domains of these functions to me;

Question 1:
f(x) = x^2 - 9

Question 2:
f(x) = | 48 - x |

Question 3:
f(x) = 8
------
x + 9

Does Question 3 equal x is a real number and x cannot equal -9?



Also I had a quick question regarding the slope of a line. I found the slope but it equals -10.5/20 do I divide from there to find the slope because then it would give me -0.525 and for some reason that doesn't look right to me.

admin answers:

1. All Real
2. All Real
3. X cannot be -9

You need to post the full question so I can help.

Joseph asks…

How to make a program to find slope and y-intercept of an equation for ti-83 calculator?

I'm trying to find M (slope) & B (y-intercept) of my equation by using a program. How do I do this??? Please help. Thanks.

admin answers:

You don't specify what your inputs are. If there are no given values, there's no way to calculate slope or a y-intercept based on no information.

Charles asks…

Find slope of the tangent line of the graph at a specific point?

Find the slope of the tangent line of the graph of f(x) = √(5x^2+4) (all under square root) at the point where x = -1
I know how to start it, but I cannot get to the answer! Please help.

admin answers:

Use the chain rule to differentiate this function. The chain rule is dy/dx = dy/du * du/dx where u is a function of x. I am using y instead of f(x).

Let u = 5x^2 + 4....................then du/dx = 10x

Let y = sqrt(u) = u^(1/2).........then dy/du = (1/2) * u^(-1/2) = (1 / sqrt(u)) =
(from the definition of u) (1 / sqrt(5x^2 + 4))

So dy/dx = (1 / sqrt(5x^2 + 4)) * 10x = (10x / sqrt(5x^2 + 4)

Where x = -1, dy/dx = ((10 * (-1)) / (sqrt(5 + 4)) = (-10 / 3)

Now we need to know the value of y where x = -1. Y = sqrt(5 + 4) = 3

So the tangent line has a slope of m = (-10 / 3) and passes through (-1,3)

y = (-10 / 3) * x + b (where b is an unknown constant).

Since this line passes through (-1,3), Substitute -1 for x and 3 for y into the above equation.

3 = ((-10 / 3) * -1) + b = +(10 / 3) + b

Subtract (10 / 3) from both sides of this equation.

3 - (10/3) = b

b = (/3) - (10/3) = (-1/3)

So the tangent line is y = ((-10 / 3) * x) - (1/3) <-------------- Answer

.

Mary asks…

How to find slope-intercept equation when given the slope and x-intercept?

Slope-intercept equation:
y=mx+b

How do you find the equation, when you are giving the slope and the x-intercept (instead of the y-intercept)?

For example, the slope is 3.0 and the x-intercept is (-2,0).

admin answers:

You can take the point-slope form of a line

(y-0) = 3 (x - (-2))

and solve it for y.

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Questions About How To Find Standard Deviation On Ti-83

Charles asks…

How do you find variance and standard deviation on a TI-83 calculator?

variance
sample variance
sample standard deviation
Those are the types of question I'm having trouble with. I need to use my calculator but don't know how. Any help would be greatly appreciated.

admin answers:

Hi

I took a look around -- the links below may be very instructional for you.


Http://www.pasles.org/Ti83.html


http://student.ccbcmd.edu/elmo/math141s/TIVideo/TIWebpage.htm


http://epsstore.ti.com/OA_HTML/csksxvm.jsp?JServSessionIdrootdlek21=6fas294qb1.n6LzoN8L/AzOnMTOogTxpQOUtxCLbx0Ka0--&jfn=ZG027E782EE618747CBDAE8D01678E37079754790182FC995934248F9FABB1F306240D91B50AE9939AC6460CBA803B0A7419&lepopus=wmB9hlGk8WUDjpUctqsI8Q3m:S&lepopus_pses=ZGC23DDB2255F665A48DC5E8BE2A5D71410D7DAAA8B8A9EB8493D3E97D5E575AE54CBB5B1BFF6572C1A058446147FAB11DDDD7DF441DCA2D9C&nSetId=98635&nBrowseCategoryId=13389&cskViewSolSourcePage=cskmbasicsrch.jsp%3FcategoryId%3D13389%26fRange%3Dnull%26fStartRow%3D0%26fSortBy%3D2%26fSortByOrder%3D1

Robert asks…

How do you find the standard deviation of a list of numbers with a Ti-83 Calculator?

I have already entered about 1200 numbers between 6 lists on my calculator and it would be really great if I could find the standard deviation without having to enter it all again somewhere else.

What would be even better would be if you could tell me how to just do a T test to compare 2 of the sets of numbers at a time. And I dont know much about calculators so step-by-step instructions would be splendid. Oh and if you could cite your source you are my new best friend, but dont worry to much about that.

Thanks in advance.

admin answers:

Actually, since you have a computer, and probably have Microsoft Office, why don't you use Excel?? It does it painlessly and you don't lose data.

Student's t test is used to compare two MEANS (averages) of two datasets. It requires essentially two factors:

1. The standard error of the mean, which is the standard deviation divided by the square root of the size of both groups (assuming equal counts)...if groups sizes are different you must determined a pooled standard error
2. The critical value of the t distribution, which is a function of the significance level (usually alpha = 0.05) and the size of the group

It also requires that all data in the sets be randomly selected and that the distribution be NORMAL: if the distribution is SKEWED, then you must use transformation methods to normalize it.

The pertinent equation is:

t (value) = difference in means / (pooled) standard error of mean

or alternatively that

t (value) * pooled standard error = difference in means

Joseph asks…

How do I find a Z-Score on a TI 83?

I know it has something to do with the normalcdf button but I just cannot remember how to freaking do it. What numbers to put where etc.

I have to find the 64th percentile Mean: 50 Standard, Deviation 7

I'm so upset it's like I did this yesterday and I just can't remember.

admin answers:

You need [2nd][Vars](Distr) > 3:invNorm(, not normalcdf(.

InvNorm(.64,50,7) should get you want you're looking for.

Betty asks…

how do i find a percentage with a mean and standard deviation?

The question states

In 1968 the group Iron Butterfly recorded the 17 minute song In-A-Gadda Vida. Most popular songs are much shorter For example, Viva La Vida by Coldplay is approximately 4 minutes long. Suppose in random sample of the length X (in munutes of songs on CDs produced by hard rock bands, x = 3.35 and s = 0.5

(a) Without assuming anything about the distribution, calculate uppoer and lower limits such that at least 75% of song lengths are between those limits. State which rule you are using and show your calculations.

(b) Assuming the data comes from a bell-shaped distribution, approximately what percentage of song lengths are expected to be more than 4.85 minutes? State which rule you are using and show your calculations.

----
I have a graphics calculator a ti-83 plus and I tried was normal probability

invnorm 75,3.35,0,5
3.687244875

i have no idea what i've done..

admin answers:

UofA, Statistical Practice I (Life Sceinces), Assignment 1, Question 3. (b)? - Oh snap!

Having the same problem too, it doesn't really seem that there's any examples relating to the question in our material... Bummer.

Lizzie asks…

Can you help me with this three part probability question?

A box contains 5 red and 7 non-red balls. Three are selected randomly, all at once. X is the number of red balls selected.

a) Write the distribution of X. Express the probabilities as fractions.

b) Show all work to find E(X).. X is not a binomial random variable. You must show the work.

c) Use your calculator to find the standard deviation of X. (What is X and how does one find the standard deviation on a TI-83??)

admin answers:

(a)
P(X = 0) = C(5,0) C(7,3) / C(12,3) = 35 / 220 = 7 / 44
P(X = 1) = C(5,1) C(7,2) / C(12,3) = 105 / 220 = 21 / 44
P(X = 2) = C(5,2) C(7,1) / C(12,3) = 70 / 220 = 7 / 22
P(X = 3) = C(5,3) C(7,0) / C(12,3) = 10 / 220 = 1 / 22

(b)
E(X) = Σ nP(X = n) for n = 0 to 3
= (0)(7/44) + (1)(21/44) + (2)(7/22) + (3)(1/22) = 5 / 4

(c)
The standard deviation is the square root of the variance, so find the variance first.

Var(X) = E(X²) - [E(X)]²

E(X²) = (0²)(7/44) + (1²)(21/44) + (2²)(7/22) + (3²)(1/22) = 95 / 44

[E(X)]² = (5/4)² = 25 / 16

Var(X) = (95/44) - (25/16) = 105 / 176

σ = √(105/176) ≈ 0.772

A TI-83 is quite handy for this kind of thing. Use the lists. The first list will have the possible values of X, and the second list has the corresponding number of possible combinations.

L1 = {0,1,2,3}
L2 = {35,105,70,10}

Now under the STAT | CALC menu:
1-Var Stats L1,L2

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