What is the distance of the two endpoints (3, 5) and (-6, -6)?

A Write the equation for line that passes through (1, 1) and (-1,7)

KengaRu [80]

Answer:y=-3x+4

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(1,1) and (-1,7).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=1.

Also, let's call the second point you gave, (-1,7), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=7.

Now, just plug the numbers into the formula for m above, like this:

m=

7 - 1

-1 - 1

or...

m=

6

-2

or...

m=-3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-3x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(1,1). When x of the line is 1, y of the line must be 1.

(-1,7). When x of the line is -1, y of the line must be 7.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,1) and (-1,7).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,1). y=mx+b or 1=-3 × 1+b, or solving for b: b=1-(-3)(1). b=4.

(-1,7). y=mx+b or 7=-3 × -1+b, or solving for b: b=7-(-3)(-1). b=4.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(1,1) and (-1,7)

is

y=-3x+4

8 0

3 years ago

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. Fo

Semenov [28]

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

The sample size is n = 14

The correlation is r = 0.65

The null hypothesis is $H_o : r < 0$

The alternative hypothesis is $H_1 : r > 0$

Generally the standard deviation is mathematically evaluated as

$Sr = \sqrt{1- r}$

$Sr = \sqrt{1- 0.65}$

$Sr = 0.616$

The degree of freedom for the one-tail test is

$df = n- 2$

$df = 14- 2$

$df = 12$

The standard error is evaluated as

$SE = \frac{0.616}{ \sqrt{12} }$

$SE =0.1779$

The test statistics is evaluated as

$t = \frac{r }{SE}$

$t = \frac{0.65 }{0.1779}$

$t = 3.654$

The p-value of of t is obtained from the z table, the value is

$p-value = P(t < 3.654) = 0.00012909$

Given that $p-value < \alpha$ then we reject the null hypothesis

Hence the company can conclude that the correlation is positive

6 0

3 years ago

How do you solve 4.0×0.7

Blababa [14]

Its 2.8, just multiply?

8 0

2 years ago

A number, x, rounded to 1 significant figure is 200 Write down the error interval for x.

makkiz [27]

Answer: 150 <= x < 250

Step-by-step explanation:

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Rounding x to 1 significant figure means that all subsequent digits after the first is rounded down to zero(0) (if the immediate number after the first is digit 5 or more, it is rounded to 1 and added to the first digit).

4 0

3 years ago

An internet company charges $8.95 per month for the first 3 months that it hosts your Web site. Then the company charges $11.95

ira [324]

Answer:

$86.60

Step-by-step explanation:

1. Subtract 8-3=5

2. Multiply 3*8.95=$26.85

3. Multiply 5*11.95=$59.75

4. Add $26.85+$59.75=$86.60

7 0

3 years ago