Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n=83, x=45, 98 percent

Could you please explain the steps and how to get to an answer? Thank you!

Answer:

(2.5,5)

Step-by-step explanation:

The x coordinate of the midpoint is found by averaging the x coordinates

(-1+6)/2 = 5/2 = 2.5

The y coordinate of the midpoint is found by averaging the y coordinates

(5+5)/2 = 10/2 = 5

A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.

To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:

n = (Z*σ/E)^2

Where:

For a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.

Plugging these values into the formula, we get:

n = (1.96*569/140)^2

n = (1114.44/140)^2

n = (7.96)^2

n = 63.4

Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.

Final answer:

To estimate the population mean with a 95% confidence level and a margin of error of $140, we use the formula n = (Z*σ/E)^2 with σ = $569. Using the z-score for 95% confidence (1.96), the calculation yields 119.44, which we round up to 120 business students needed for the sample.

Explanation:

Calculating Minimum Sample Size for Estimating a Population Mean

To determine the minimum sample size needed to estimate the mean monthly earnings of business students at one college with 95% confidence and a margin of error of $140, we use the formula for the sample size (n). The formula is derived from the properties of a normal distribution and the central limit theorem and is as follows:
n = (Z*σ/E)^2
where:
Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence),
σ (sigma) is the population standard deviation, and
E is the desired margin of error.

Plugging in the given values of σ = $569 and E = $140, we find:
n = (1.96 * 569 / 140)^2
n ≈ (10.924)^2
n ≈ 119.44

Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, 120 business students must be randomly selected to achieve the desired precision.

The correct options are:

A, C and E.

Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many categories. The forms are often enclosed by an outline or border that is composed of points, lines, curves, etc.

As per the given data:

We are given some shapes in the diagram, and we are also given the type of the shape, we have to identify the correct options out of the given options.

Figure A is a cylinder.

This is correct, as the figure correctly resemble a cylinder.

Figure B is a square pyramid.

This is incorrect, as the figure resembles a cone.

Figure C has no bases.

This is correct, as the figure correctly resemble a sphere and it has no base.

Figure D is a triangular prism.

This is incorrect, as the figure resembles a rectangular prism.

Figure D has four lateral faces that are triangles.

This is correct, as the figure correctly resemble a rectangular prism with four lateral faces that are triangles.

Hence, the correct options are:

A, C and E.

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Answer:

I believe it is standard form?

Step-by-step explanation:

Answer:  y= - 2(x - 3)(x+5)​  is Factored form

Step-by-step explanation: Quadratic equation forms

Vertex form is y = a(x -h)² + k

Standard form is   y = ax² + bx + c

Factored form is [tex]y = a(x + r_{1} )(x + r_{2} )[/tex]

Answer:

1. 0.869 = 86.9% probability that an average American adult watches more than 300 minutes of television per day.

2. 100% probability that an average American adult watches more than 2,000 minutes of television per week.

Step-by-step explanation:

To solve this question, we need to understand the poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.

Normal distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

To approximate the Poisson to the normal, we use [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]

1. Find the probability that an average American adult watches more than 300 minutes of television per day.

The mean is 320 minutes per day, so [tex]\lambda = 320, \mu = 320, \sigma = \sqrt{320} = 17.89[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 300. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{300 - 320}{17.89}[/tex]

[tex]Z = -1.12[/tex]

[tex]Z = -1.12[/tex] has a pvalue of 0.131.

1 - 0.131 = 0.869

0.869 = 86.9% probability that an average American adult watches more than 300 minutes of television per day.

2. Find the probability that an average American adult watches more than 2,000 minutes of television per week.

A week has 7 days, so [tex]\lamda = 7*320 = 2240, \mu = 2240, \sigma = \sqrt{2240} = 47.33[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 2000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2000 - 2240}{47.33}[/tex]

[tex]Z = -5.07[/tex]

[tex]Z = -5.07[/tex] has a pvalue of 0

1 - 0 = 1

100% probability that an average American adult watches more than 2,000 minutes of television per week.

Answer:

largest area that can be enclosed = 8,000,000 m²

Step-by-step explanation:

Since it is a rectangle plot, the area is expressed as; A = xy, where x is length and y is width.

Because it is next to the river, he only needs to fence three sides, so amount of fencing; F = x + 2y.

Since we know the amount of fencing available is 8000m, we get:

8000 = x + 2y

solving for x, we have;

x = 8000 - 2y

substitute 8000 - 2y for x into the area equation to give;

A = (8000 - 2y)y distribute

A = -2y² + 8000y

Now, due to the negative sign next to 2, this will be a parabola which opens down, meaning that the point of maximum area will be at the vertex,

Thus; y = -b/2a = -8000/[2(-2)] = 2000

x = 8000 - 2(2000) = 4000

A = 4000(2000) = 8,000,000 m²

Answer:

22%

Step-by-step explanation:

Answer:

22% tax bracket

Step-by-step explanation:

Answer:

Step-by-step explanation:

let width=x

length=x+4

height=x-2

A=W×L

252=(x)(x+4)

252=x^2 +4x

0=x^2 +4x -252

use quadratic formula

x=14

W=14

L=18

H=12

V=W×L×H

V=(14)(18)(12)

Final answer:

To calculate the volume of the crate, solve for the width using the base area and the relation between length and width, then find the height. Multiply length, width, and height to obtain the crate's volume.

Explanation:

To find the volume of the crate, we must first determine the dimensions of the base. We know that the area of the base is 252 square inches, and that the length (L) is 4 inches greater than the width (W).

Therefore, we can express the length as L = W + 4. Since the area of a rectangle is given by length times width (A = L × W), we can write the equation W × (W + 4) = 252.

Step 1: Find the width (w)

Substitute l=w+4 into the first equation:

w² + 4w - 252= 0

Solve the quadratic equation using the quadratic formula:

w = −b ±√ b²−4ac​​/2a

where a=1, b=4, and c=−252.

w = −4 ± √4²−4 × 1 × −252​​/2 × 1

w = −4 ± √1024​​/2

w = −4 ± 32​/2

Since the width cannot be negative, we discard the negative solution.

Therefore, w=14 inches.

Step 2: Find the length (l) and height (h)

l=w+4=14+4=18 inches

h=w−2=14−2=12 inches

Step 3: Find the volume (V)

V = l × w × h = 18 × 14 × 12 = 3024 cubic inches.

The requried, Il. The voluntary response makes it likely that the most dissatisfied people were the ones to respond. Ill. The response suffers from under coverage. are true. Option A is correct.

The survey is defined as an activity that took the participation of the public in order to improve the service by taking feedback from the targeted public.

here,
As of the given conditions,
The number of people that returned the voluntaries is not a very large number, while the voluntary response increases the likelihood that the most dissatisfied people responded, the response also suffers from under coverage

.

Thus, Both II and III are correct statements. Option A is correct.

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Answer:

$780 to $1100

Step-by-step explanation:

A confidence interval has two bounds. A lower bound and an upper bound. They are dependent of the sample mean and of the margin of error M.

In this problem:

Sample mean: $940

Margin of error: $160

The lower end of the interval is the sample mean subtracted by M. So it is 940 - 160 = $780

The upper end of the interval is the sample mean added to M. So it is 940 + 160 = $1100

So the answer is

$780 to $1100

Answer:

[tex]940-160=780[/tex]

[tex]940+160=1100[/tex]

So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100

Step-by-step explanation:

For this case we can define the following random variable X as the monthly rent and we know the following properties given:

[tex]\bar X= 940 [/tex] represent the sample mean

[tex] ME = 160[/tex] represent the margin of error

n = 10 represent the sample size

The confidence interval for the true mean is given by:

[tex] \bar X \pm z_{\alpha/2} \sqrt{\frac{\sigma}{\sqrt{n}}}[/tex]

And is equivalent to:

[tex]\bar X \pm ME[/tex]

And for this case if we replace the info given we got:

[tex]940-160=780[/tex]

[tex]940+160=1100[/tex]

So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100

Answer:

That should be pentagon, irregular

(5 sides which are not equal)

Hope this helps!

:)

Answer:

0.104 (10.4%)

Step-by-step explanation:

[tex]UCL = \bar{p}+z(\sigma)[/tex]

[tex]\sigma = p(1-)) Vn = 1.02(1-202)) 5[/tex] = 0.028

[tex]\thereforeUCL = .02+(3x0.028)[/tex] = 0.104

[tex]\thereforeUCL[/tex]= 10.4%

Answer:

- The integral of arctan(x)/x =

C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).

- The radius of convergence is R = 1/x

Step-by-step explanation:

First note that

tan^(-1)x = arctan(x)

And

arctan(x) = Σ [(-1)^n. x^(2n+1)]/(2n+1). From n = 0 to infinity

arctan(x)/x = Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity

∫arctan(x)/x dx = ∫{Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity}dx

= ∫{Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.∫x^(2n)dx

= {Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.x^(2n+1)/(2n+1) + C

= C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).

To obtain the radius of convergence, we apply the ration test

R = Limit as n approaches infinity |a_n/a_(n+1)|

a_n = (-1)^n.x^(2n+1)]/(2n+1)²

a_(n+1) = (-1)^(n+1).x^(2(n+1)+1)]/(2(n+1)+1)²

|a_n/a_(n+1)| = (2(n+1) + 1)²/(2n+1)².x

= (1/x)[1 + 2/(2n+1)]

R = Limit as n approaches infinity |a_n/a_(n+1)|

= R = Limit as n approaches infinity (1/x)[1 + 2/(2n+1)]

R = 1/x

The integration of the arctan (x)/x is C + Σ [(-1)^n x^(2n+1)]/(2n+1)² where n is from 0 to ∞. The radius of convergence is R = 1/x

It is the reverse of differentiation.

The indefinite integral is a power series that will be

[tex]\rm \int \dfrac{\tan^{-1}x }{ x} \ dx[/tex]

We know that the arctan is given as

[tex]\rm \tan^{-1} x = \dfrac{\sum [(-1)^n \ x^{2n+1}]}{(2n+1)}\\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ x^{2n})]}{(2n+1)}\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n}[/tex]

Then we have

[tex]\rm \int \dfrac{\tan^{-1} x }{x}\ dx= \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n} dx\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \int x^{2n}\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)^2} x^{2n + 1} + C[/tex]

To obtain the radius of convergence, then the ration test

[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{a_n}{a_{n+1}}\\\\\\a_n = \dfrac{(-1)^n \ x^{2n+1} }{(2n+1)^2}\\\\\\a_{n+1} = \dfrac{(-1)^{n+1} \ x^{2(n+1)+1} }{(2(n+1)+1)^2}\\\\\\ \dfrac{a_n}{a_{n+1}} = \dfrac{1}{x}(1+\dfrac{2}{2n+1})[/tex]

Then we have

[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{1}{x}(1+\dfrac{2}{2n+1})\\\\\\R = \dfrac{1}{x}[/tex]

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Answer:

The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Step-by-step explanation:

Let the random variable X represent the lengths of the classes.

The random variable X is uniformly distributed within the interval 49.0 and 54.0 minutes.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:

[tex]P(50.75<X<51.25)=\int\limits^{51.25}_{50.75}{\frac{1}{54-49}}\, dx\\\\=\frac{1}{5}\times [x]^{51.25}_{50.75}\\\\=\frac{51.25-50.75}{5}\\\\=0.10[/tex]

Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Answer: 0.050

I just did it and i got it right.

Answer:

A) 0.015

B) 4 bous6

Step-by-step explanation:

That at most 2 of the selected children are male means that number of male must be less than or equal to 2

Pr (male) = 0.506

Pr (female) = 0.494

Pr (at most 2 males) = 0.506 x 0.506 x 0.494 x 0.494 x 0.494 x 0.494 = 0.015

Expected number of boys in a randomly selected number of 6 is

0.506 x 6 = 3.03

We round off to 4 boys

Answer: 9

Step-by-step explanation:

In order to make the expression a perfect square, ,we ate going to add to the expression the square of the half of the coefficient of 6.

x² + 6x + c

= x² + 6x + (6/2)²

= x² + 6x + 3²

= x² + 6x + 9

Therefore, 9 is the required solution that will.make the expression a perfect square.

Answer:

9

Step-by-step explanation.

x² + 6x + 9

= (x+3)(x+3)

= (x + 3)²

it is a perfect square trinomial when c is equal to 9

Answer:

Step-by-step explanation:

The question is incomplete because the data is missing, i.e. the probability that you will score 5, 4, 3, 2, 1.

But it is resolved as follows:

[tex]P(x\geq 3) = P(\frac{x - m}{\frac{sd}{\sqrt{n} } } \geq \frac{3 - m}{\frac{sd}{\sqrt{n} }})\\\\[/tex]

where m is the mean and sd is the standard deviation.

the m is calculated by the sum of the multiplication of the score by the probability of this  

that is to say,  

score   probability

  5           0.2

  4           0.3

  3            0.1

  2           0.3

  1             0.1

m = 5*0.2 + 4*0.3 + 3*0.1 + 2*0.3 + 1*0.1

m = 3.2  

However, the standard deviation will be calculated by

sd = [tex]\sqrt{\\}[/tex]∑[tex](x - m)^{2}*p[/tex]

that is, knowing the mean already, we can calculate the standard deviation, following the example:

sd =[tex]\sqrt{[(5-3.2)^2] *0.2 + [(4-3.2)^2] *0.3 + [(3-3.2)^2] *0.1 + [(2-3.2)^2] *0.3 + [(1-3.2)^2] *0.1 }[/tex]

sd = [tex]\sqrt{1.76}[/tex]

sd = 1.327

And also n = 5, because it's 5 scores. We replace in the initial equation:

[tex]P(x\geq 3) = P(Z \geq \frac{3 - 3.2}{\frac{1.327}{\sqrt{5} }})\\\\[/tex]

[tex]P(x\geq 3) = P(Z \geq -0.337)\\\\\\[/tex]

Therefore for the example the number z is -0.337, which if in the normal distribution table corresponds to 0.3520, that is the probability that the average is at least 3, for the example is 35.20 %.

Answer:

87.7 degrees.

Step-by-step explanation:

In triangle ABC, attached.

The height of the building |AB|=443 meters

The distance of the agent across the street , |BC|=18 meters

We want to determine the angle at C.

Now,

[tex]Tan C=\dfrac{|AB|}{|BC|} \\C=arctan (\dfrac{|AB|}{|BC|} )\\=arctan (\dfrac{443}{18} )\\=87.67^\circ\\\approx 87.7^\circ $(correct to the nearest tenth)[/tex]

The agent should sfoot his laser gun at an angle of 87.7 degrees.

Answer: A, D, E

Step-by-step explanation

Answer:

No

Step-by-step explanation:

I got it right on Instruction

Answer:

its No trust me

Step-by-step explanation:

For a positive angle coterminal to 127°, select Graph B (with angle measurement of 492°). For the angle 79°, the nearest two positive coterminal angles are 439° and 799°, and the nearest two negative coterminal angles are -281° and 79°.

A positive angle coterminal to 127° can be found by adding 360° to it, since coterminal angles are separated by full rotations:

1.First Positive Coterminal Angle:

 [tex]\( 127° + 360° = 487° \)[/tex] (This is not one of the choices provided.)

2.Second Positive Coterminal Angle:

  [tex]\( 487° + 360° = 847° \)[/tex] (This is beyond the range of the options provided.)

However, if we look for a coterminal angle between 360° and 720°, we find:

 [tex]\( 127° + 360° = 487° \)[/tex], which is closer to 492° given in Graph B.

For the angle 79°:

1.Positive Coterminal Angles:

  - Add 360° for the first positive coterminal angle:

    [tex]\( 79° + 360° = 439° \)[/tex]

  - Add another 360° for the second positive coterminal angle:

 [tex]\( 79° + 720° = 799° \)[/tex]

2. Negative Coterminal Angles:

  - Subtract 360° for the first negative coterminal angle:

   [tex]\( 79° - 360° = -281° \)[/tex]

  - Subtract 720° for the second negative coterminal angle:

    [tex]\( 79° - 720° = -641° \)[/tex] (However, this is not the nearest negative coterminal angle.)

The first negative coterminal angle is already the nearest, so the second negative coterminal angle is actually the original angle itself, which is 79° (since subtracting 0° gives us the same angle).

So, the nearest two positive coterminal angles are 439° and 799°, and the nearest two negative coterminal angles are -281° and 79°.

complete question given below:

Answer:

7.4

Step-by-step explanation:

To calculate the time taken to travel a certain distance at a certain speed, use the formula: Time = Distance/Speed. In this case, to travel 520 miles at 70 miles per hour, it would take approximately 7.43 hours or 7 hours and 26 minutes.

The subject of this question is about calculating time based on speed and distance in a real-world context. To find out how many hours it will take you to reach your destination travelling at 70 miles per hour for 520 miles, we use the formula: Time = Distance / Speed. In this context, the distance is 520 miles and the speed is 70 miles per hour. Insert these values into the formula, you get: Time = 520 / 70 which gives you approximately 7.43 hours. This means it would take you about 7 hours and 26 minutes to reach your destination, if you were traveling at a consistent speed of 70 miles per hour.

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Answer:

The answer is B

Step-by-step explanation:

The required value of the quadratic function which is determined by the using quadratic formula would be [tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]   which is the correct answer would be an option (B).

The quadratic function is defined as a function containing the highest power of a variable is two.

We have been given that quadratic function as

5x = 6x² – 3

⇒ 6x² - 5x  - 3 = 0

Compare the given function to the standard quadratic function

f(x) = ax² + b x + c = 0.

We get a = 6, b = -5 and c = -3

Using the quadratic formula to solve the above quadratic function

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 6, b = -5 and c = -3 in the quadratic formula

[tex]x = \dfrac{-(-5)\pm\sqrt{-5^2-4\times6\times-3}}{2\times6}[/tex]

[tex]x = \dfrac{5\pm\sqrt{25+72}}{12}[/tex]

[tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]

Therefore, the correct answer would be an option (B).

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Answer:

WHAT IS THE QUESTION WHAT IS X IN WHAT EQUATION!!!!!!!!

Step-by-step explanation:

Answer:

plzz i asked for brainliest on ur other question

Step-by-step explanation:

Answer:

100000

Step-by-step explanation:

[tex] {10}^{5} = 100000[/tex]

[tex]10 \times 10 \times 10 \times 10 \times 10 = 100000[/tex]

Answer:

506.58

Step-by-step explanation:

Your welcome ;w;

Answer:

21 sq ft

Step-by-step explanation:

The formula is 0.5bh; b is the length of the base (6) and h is the height (7). So if you plug in those values, you have 0.5(6)(7). Multiply those and you get 21!

Answer:

The area of the triangle is 21 ft (640.08 centimeters)

The area of the rectangle is 120 ft (3657.6 centimeters)

The area of the whole figure is 141 ft (4297.68 centimeters)

Step-by-step explanation:

The area of a triangle is:

[tex]A = \frac{1}{2}bh[/tex]  b is the base and h is the height.

Plug in what you have

[tex]A= \frac{1}{2}(6)(7)[/tex] multiply 6 by 7

[tex]A = \frac{1}{2} (42)[/tex] divide 42 by 2

[tex]A = \frac{42}{2}[/tex]

[tex]A = 21[/tex]

Now you have to find the area of the rectangle

The area of a rectangle is:

A = bh

Plug in what you have

A = (10)(12)

A = 120

Now add both areas together to get the area of the whole figure

120 + 21 = 141

Answer:

12.55

Step-by-step explanation:

Answer:

[tex]Area\,\,of\,\,the\,\, circle=12.56\,\, units ^2[/tex]

Step-by-step explanation:

Circumference of the circle= 12.56 units

[tex]Circumference=2\times\pi \times r[/tex]

As,

[tex]\pi =\dfrac{22}{7}=3.14[/tex]

     [tex]2\pi r=12.56\\\\2\times 3.14 \times r=12.56\\\\6.28\times r=12.56\\\\r=\dfrac{12.56}{6.28} \\\\r=2\,\,units[/tex]

Area of a circle= [tex]=\pi \times r^2[/tex]

                        [tex]=3.14\times 2^2\\\\\=3.14\times 4\\\\=12.56\,\, units ^2[/tex]

Answer:

y=2x+1

Step-by-step explanation:

A(1;3)  and m=2

y-yA=m(x-xA)

y-3=2(x-1)

y-3=2x-2

y=2x+1; or 2x-y+1=0