Answers
The pairs of linear equations that are parallel are:
2 and 4.
Which pair of lines are parallel?Two linear equations:
y = a*x + b
y = c*x + d
Are parallel if the two slopes are equal and the y-intercepts are different, then:
a = c
b ≠ d
Let's write all the lines in the slope-intercept form:
1) 4x + 3y = 15
3y = 15 - 4x
y = (-4/3)*x + 15/3
y = (-4/3)*x + 5
2) 3x - 4y = -8
-4y = -8 - 3x
y = 2 + (3/4)x
So we can see that lines 2 and 4 are parallel.
If we rewrite line 3 we will get:
y + 1 = (4/3)*(x - 6)
y = (4/3)*x - 8 -1
y = (4/3)*x - 9
Then we conclude that only lines 2 and 4 are parallel.
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Related Questions
Solve the inequalities
Answers
Answer:
m ≥ 6
Step-by-step explanation:
The question asks us to solve the following inequality:
[tex]8m - 8 \geq 40[/tex].
To solve it, we need to make m the subject of the inequality:
[tex]8m - 8 \geq 40[/tex]
⇒ [tex]8m - 8 + 8 \geq 40 + 8[/tex] [Adding 8 to both sides of inequality]
⇒ [tex]8m \geq 48[/tex]
⇒ [tex]\frac{8}{8}m \geq \frac{48}{8}[/tex] [Dividing both sides of inequality by 8]
⇒ [tex]m \geq \bf 6[/tex]
Therefore, the solution to the inequality is m ≥ 6.
a hotel is looking over its occupancy, the number of rooms sold, over the course of the last 20 days. the data are provided below. use excel and the quartile.inc function to construct a box and whisker plot for the dataset. what is the interquartile range? round your answer to two decimal places. hotel occupancy 131 135 139 124 124 121 124 135 124 helpcopy to clipboarddownload csv provide your answer below:
Answers
The interquartile range is 16.00
To construct a box and whisker plot in Excel using the Quartile.INC function for the given data, follow these steps:
1) Enter the data into a column in Excel.
2) Select the data column and click on the "Insert" tab in the top menu.
3) Click on "Insert Statistic Chart" and select "Box and Whisker" from the dropdown menu.
4) In the "Chart Elements" menu on the right, click on the arrow next to "Axis Titles" and select "Primary Vertical Axis Title" to add a title for the y-axis.
5) Label the y-axis "Number of Rooms Sold".
6) Right-click on the y-axis and select "Format Axis" from the dropdown menu.
7) In the "Number" menu, select "Number" as the category and set the number of decimal places to 0.
8) In the "Chart Elements" menu, click on the arrow next to "Chart Title" and select "None" to remove the chart title.
9) The resulting box and whisker plot should show the quartiles, the median, and any outliers.
To find the interquartile range, subtract the first quartile (Q1) from the third quartile (Q3). The Quartile.INC function in Excel returns the exclusive quartiles (i.e., does not include the median in either quartile), so the interquartile range is calculated as:
IQR = Q3 - Q1
Using the Quartile.INC function with the given data, we get:
Q1 = 78.5
Q3 = 94.5
Therefore, the interquartile range is
IQR = Q3 - Q1 = 94.5 - 78.5 = 16
Rounding to two decimal places, the interquartile range is 16.00.
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f(x) = -3x + 2 f(7) =
Answers
The value of the function is -19.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -3x + 2
Substitute x = 7.
f(7) = -3 x 7 + 2
f(7) = -21 + 2
f(-7) = -19
Thus,
-19 is the value.
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Let t
be the time in weeks. At time t=0
, organic waste is dumped into a pond. The oxygen level in the pond at time t
is given by
f(t)=t2−t+1t2+1
.
Assume f(0)=1
is the normal level of oxygen.
(a) On a separate piece of paper, graph this function.
(b) What will happen to the oxygen level in the lake as time goes on?
The oxygen level will eventually return to its normal level in the long-run.
(c) Approximately how many weeks must pass before the oxygen level returns to 75
% of its normal level?
weeks (Round to at least two decimal places.)
Answers
The graph is plotted and attached
The oxygen level will be increasing as time goes on
In 0.5 weeks the oxygen level will return to 75% of its normal level
What will happen to the oxygen level in the lake as time goes on?This is the end behavior of the graph, of the function f(t) = t^2 − t + 1, the graph shows that as t tends to infinity. the oxygen level will continue to increase.
The graph is plotted and attached
From the problem. the normal level of oxygen is at f(0) = 1
75% of 1 = 0.75
From the graph, the oxygen level will return to normal level in 1 week(1, 1) and at 0.5 the oxygen level is 0.75, (0.5,0.75). This is the vertex of the graph.
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create a file lab2.py and define three classes, polygon, rectangle, triangle (see next page for a visual representation)
Answers
Lab2.py is a Python script that creates and manipulates three custom classes. The classes are as follows:
1. Person: This class stores information about a person, such as their name and age.
2. Student: This class inherits from the Person class and adds additional information, such as the student's major and GPA.
3. Instructor: This class also inherits from the Person class and adds additional information, such as the instructor's department and course load.
A file lab2.py and define three classes, polygon, rectangle, triangle is:
class Polygon:
def __init__(self, number_of_sides):
self.number_of_sides = number_of_sides
class Rectangle(Polygon):
def __init__(self, length, width):
Polygon.__init__(self, 4)
self.length = length
self.width = width
def area(self):
return self.length * self.width
class Triangle(Polygon):
def __init__(self, base, height):
Polygon.__init__(self, 3)
self.base = base
self.height = height
def area(self):
return 0.5 * self.base * self.height
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What is the volume of this right cone?
O 40 cm³
O 300 cm³
O 400 cm³
O 480 cm³
15.6 cm
12 cm
10 cm
Answers
The volume of the right cone is (c) 400π cm cube
How to determine the volume of the coneFrom the question, we have the following parameters that can be used in our computation:
Radius = 10 cm
Height = 12 cm
The volume of the cone is calculated as
Volume = 1/3πr²h
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3π * 10² * 12
Evaluate
Volume = 400π
Hence, the volume is 400π cm cube
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14. Cheyenne took a train to visit her aunt. The train traveled at a constant speed of 60 miles per hour. Complete the table, and then write an equation to find the total distance, d, traveled after t hours.
Answers
The equation to find the total distance would be 60t.
What is total distance?
Whole distance refers to the actual distance between the origin and destination locations of the substance.
The distance traveled is equal to the speed multiplied by the time traveled, which gives the formula:
d = 60t
where d is the total distance traveled in miles, and t is the time traveled in hours.
Therefore, The equation to find the total distance would be 60t.
The table is below:
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Compute the probability of randomly drawing six cards from a standard deck of cards and getting four aces and two kings. Give your answer accurate to at least eight decimal places. Compute the probability that a five-card poker hand is dealt to you that contains all hearts. Give your answer accurate to at least six decimal places.
Answers
The probability of being dealt a five-card poker hand that contains all hearts is approximately 0.000495, or 0.0495%.
Probability is the measure of the likelihood of an event happening, and it is expressed as a number between 0 and 1. The closer the number is to 0, the less likely the event is to occur, and the closer it is to 1, the more likely it is to occur.
Now, let's look at the first question: what is the probability of drawing six cards from a standard deck of cards and getting four aces and two kings?
So, the number of combinations of six cards from a deck of 52 cards is:
52C6 = 52!/6!(52-6)! = 20,358,520
Next, we need to find out how many ways we can draw four aces and two kings from the deck. There are 4 aces and 4 kings in a standard deck of cards, so the number of ways to draw four aces and two kings is:
4C4 x 4C2 = 1 x 6 = 6
The first factor, 4C4, represents the number of ways to draw all 4 aces, and the second factor, 4C2, represents the number of ways to draw 2 kings from the remaining 4 kings.
Finally, we can calculate the probability of getting four aces and two kings by dividing the number of ways to draw four aces and two kings by the number of combinations of six cards from the deck:
P(four aces and two kings) = 6/20,358,520 = 0.000000294
So, the probability of randomly drawing six cards from a standard deck of cards and getting four aces and two kings is approximately 0.00000029, or 0.0000294%.
Now, let's move on to the second question: what is the probability that a five-card poker hand is dealt to you that contains all hearts?
In a standard deck of cards, there are 13 hearts and 52 cards in total, so the probability of drawing one heart from the deck is 13/52, or 1/4. The probability of drawing five hearts in a row is the product of the probabilities of drawing each heart, since each card is drawn without replacement:
P(five hearts) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.000495
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The area of this triangle is 64.8 km². Find the height h.
18 km is the base.
The height of the triangle is?
Answers
Answer: 16.2 km
Step-by-step explanation:
The height of the triangle can be found using the area formula for triangles:
Area = (1/2) × base × height
Rearranging the formula to solve for the height gives:
height = (2 × Area) / base
In this case, the area of the triangle is 64.8 km² and the base is given as 8 km. So, the height of the triangle can be calculated as:
height = (2 × 64.8 km²) / 8 km
height = 16.2 km
Answer:
7.2 km
Step-by-step explanation:
the formula for the area of a triangle is 1/2*b*h where b is its base and h is its height. now let's solve for the height
64.8=1/2*18h
64.8=9h
64.8/9=h
7.2 km=h
Identifying a Graph from an Equation
Which graph represents a function with amplitude 4 and period pi?
Answers
The graph of the function f(x) = 4sin(2x) is illustrated in the image.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
We know sin(x) is a periodic function with amplitude 1 and a period of 2π.
Therefore, A periodic function with amplitude 4 and period π would be,
f(x) = 4sin(2x).
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commutative property of (32)-5+7?
Answers
Answer:
= 34
Step-by-step explanation:
(32)-5+7
32 - 5 + 7
= 32 + 2
= 34.
Find a quadratic equation with integer coefficients that has the given solution set.
{-10, 9}
Answers
The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
If the given solution set is {-10, 9}.
Then the quadratic equation can be written in factored form as:
(x + 10) (x - 9) = 0
Expanding the product,
x² + x - 90 = 0
Therefore,
The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.
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A group of friends’ dinner bill is $82.95 They want to leave a 15% tip. What is their total dinner bill, including tip?
Answers
The total dinner cost, including the tip, comes at $92.40.
What is the percentage of a number explained?The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals.A sum is considered to be made up of 100 equal parts when expressed as a percentage. Use the symbol% to denote percentages in numbers.A lunch for a few friends will set you back $82.95
They want to leave a 15% tip.
So,
Amount of tip:
15 % of 82.95 = 15*82.95 / 100
15 % of 82.95 = 12.4425
Total cost = 82.95 + 12.4425
Total cost = 95.3925
Total cost = $92.40
Thus, the total dinner cost, including the tip, comes at $92.40.
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a cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.
Answers
The angular speed in radians per minute of the cyclist riding a bike with wheels of diameter 26 inches at a speed of 22 miles per hour is approximately 1124.65 radians per minute.
The formula for the angular speed is:
angular speed = linear speed / radius
where the radius is half the diameter of the wheel. We need to convert the units to be consistent, so let's convert the speed from miles per hour to inches per minute and the diameter from inches to feet:
22 miles per hour = 22 * 5280 feet per hour / 60 minutes per hour
≈ 2437.3 inches per minute
26 inches = 26/12 feet = 2.1667 feet
Now we can calculate the angular speed:
angular speed = 2437.3 / 2.1667 ≈ 1124.65 radians per minute
Your question is incomplete, most likely it was:
A cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.
Find the angular speed in radians per minute.
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1. Which of the following is not a variable cost?
A. wages paid to labor
B. seeds and fertilizers for paddy farmers
C. rent on land
D. electricity bills
Answers
Answer:
b
Step-by-step explanation:
b seeds snd fertilizer
Stacy says there is not enough information to prove that ACXBCX. Explain why Stacy's statement is incorrect.
Answers
Stacy's statement is incorrect because Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.
Reflexive Property of Congruence:
An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence. Together with the two given angle congruencies, we can conclude that by ASA.Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.
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(15x²+x²+7)-(6x² - 2x³)-7x²
Answers
Answer:
= 3x² + 7 +2x³.
Step-by-step explanation:
Here is my solution to my answer.
If △ EFG ∼ △ ABC
, What value of x will make the two triangles similar?
Answers
Answer:
the value of x will be 9 they all are similar so we will just take ratios and do cross multiplication
Craig forgot to record the amount of the check he wrote to the hardware store. The statement from his bank shows an ending balance
of $521.60. What is the amount of the check Craig wrote to the hardware store? Define a variable for the unknown quantity. Write and
solve an equation to answer the question.
Answers
Answer: Let's call the amount of the check Craig wrote to the hardware store "x".
According to the problem, the statement from Craig's bank shows an ending balance of $521.60. This means that his balance before writing the check was $521.60 + x.
So, we can write the equation:
$521.60 + x = $521.60
Subtracting $521.60 from both sides:
x = 0
This means that Craig's check was for $0.
Step-by-step explanation:
he auditors for a health insurance company are reviewing the bills from client's stays at hospitals from last year. the length of stay in days for hospital visits from 20 randomly sampled bills is provided below. use excel and the quartile.inc function to construct a box and whisker plot for the dataset. what is the value of the third quartile? round your answer to two decimal places. hospital length of stay (days) 7 6 7 6 7 8 3 2 6 provide your answer below:
Answers
The value of the third quartile is approximately 7.00, rounding it up to two decimal places.
In order to construct a box and whisker plot using Excel and the QUARTILE.INC function we will follow the steps -
Enter the data into a column in Excel.Select the column of data.Click on the "Insert" tab and select "Insert Statistic Chart."Choose "Box and Whisker" from the chart types.The box and whisker plot will be displayed.Using the given data, the third quartile (Q3) can be found using the QUARTILE.INC function in Excel as follows -
Enter the data into a column in Excel.Use the formula =QUARTILE.INC(data, 3) to find the third quartile (Q3).Using this method, rounding the result to two decimal places we get,
Q3 = QUARTILE.INC({7, 6, 7, 6, 7, 8, 3, 2, 6}, 3)
Q3 ≈ 7.00 (rounded to two decimal places)
Therefore, the value of the third quartile is approximately 7.00.
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What can be combined with 2x2? Select
all that apply.
Answers
Answer:
its only -11x^2
Step-by-step explanation:
2x^2 and -11x^2 have the same variable.
Identify the function of the figure below this is trigonometry by the way
Answers
The graph shown is the graph of the cotangent function.
What is the graph of Cotangent?
The graph of the cotangent function, cot(x), is a periodic function that has a period of 2π. The cotangent function is the reciprocal of the tangent function, so its graph is related to the graph of the tangent function.
Like the tangent function, the cotangent function has singularities at x = (n + 1/2)π where n is an integer. At these points, the function has a vertical asymptote, meaning it approaches positive and negative infinity as x approaches (n + 1/2)π from either side.
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59.05 as a fraction of an hour
Answers
The given decimal in fraction as 1181/20.
What is conversion of decimal number to fraction?Steps for conversion:
Identify the place value of the digits after the decimal, in the number.Use that to determine what the denominator of the fraction would be.Remove the decimal point. Re-write in the fraction form and simplify itExpress in terms of the lowest equivalent fraction.The given decimal number is 59.05
Here, multiply 100 to both the numerator and denominator of the decimal, that is
59.05/1 ×100/100
= 5905/100
= 1181/20
Therefore, the fraction is 1181/20.
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How do you find a percentile of normal distribution (probability, probability theory, probability distributions, normal distribution, math)?
Answers
To find the percentile of a normal distribution, first determine the mean, then convert the interested value to a standard score, look-up the normal distribution table to find the area to the left of the normal score. Finally, multiply the area by 100.
Steps to find the percentile of a normal distributionDetermine the mean (μ) and standard deviation (σ) of the normal distribution.Convert the value you are interested in (i.e., the score) to a standard score (z-score) using the formula:z = (x - μ) / σ
where x is the value of interest.
Look up the z-score in a standard normal distribution table to find the area (probability) to the left of the z-score.Multiply the area by 100 to get the percentile.For example, suppose you want to find the percentile of a test score of 85, which comes from a normal distribution with a mean of 75 and a standard deviation of 10.
The mean (μ) is 75 and the standard deviation (σ) is 10.The z-score for a test score of 85 is:z = (85 - 75) / 10 = 1
Using a standard normal distribution table, we can find that the area to the left of a z-score of 1 is 0.8413.To find the percentile, we multiply the area by 100:0.8413 * 100 = 84.13
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A jug contained314 pints of milk at the start of a baking class. At the end of the class, only 3 fluid ounces were left.
How many fluid ounces of milk were used during the class?
Responses
10 fl oz
10 fl oz
23 fl oz
23 fl oz
49 fl oz
49 fl oz
101 fl oz
Answers
Answer:
311 fl oz only were used, that is what I got for your answer..
The answer is 49 fl oz
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answers
The value of the equation is 4.19p = -6.1
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
2.3p - 10.1 = 6.5p - 4 - 0.01p
On simplifying , we get
Adding 4 on both sides , we get
2.3p - 6.1p = 6.49p
Subtracting 2.3p on both sides , we get
4.19p = -6.1
Now , the value of the equation similar to 4.19p = -6.1 is 2.3p - 6.1p = 6.49p
Hence , the equation is 4.19p = -6.1
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A line passes through point (-6, 1)and has a slope of 3. Write an equation in Ax+By=Cform for this line. CO Use integers for A, B, and C.
Answers
An equation in Ax + By=C form for this line include the following: -3x + y = 19.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (-6, 1), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (1) = 3(x - (-6))
y - 1 = 3x + 18
y = 3x + 18 + 1
y = 3x + 19
In standard form, we have:
-3x + y = 19.
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A car tire company is testing a new tire that has proposed improved performance in wet conditions. An experiment was performed on a closed, half-mile track in wet conditions with the same car and driver. Two trials were performed with standard and new Wet Condition tires. What would the tire company MOST LIKELY infer based on this data?
Responses
A There is no hypothesis provided.There is no hypothesis provided.
B The hypothesis was neither verified or refuted.The hypothesis was neither verified or refuted.
C The hypothesis of the company is refuted.The hypothesis of the company is refuted.
D The hypothesis of the company is verified.
Answers
Answer:
B
Step-by-step explanation:
Based on the information provided, it is not possible to determine the hypothesis of the tire company. Therefore, options C and D can be eliminated.
Option A suggests that no hypothesis was provided, which may be possible. However, it is implied that the hypothesis was related to the proposed improved performance in wet conditions of the new tire. Therefore, option A may not be the best answer.
Option B suggests that the hypothesis was neither verified nor refuted. This is a common outcome in many experiments, and it is possible that the tire company may draw this conclusion based on the data. Therefore, option B is the most likely answer.
So, the tire company MOST LIKELY would infer that the hypothesis was neither verified nor refuted based on this data.
Which of the following are like terms?
Select 3 correct answer(s)
Question 1 options:
3x2 & 3x4
3x4 & 2x4
3y2 & 3x2
2x2 & 3x2
x2 & y2
2x & 3x
4x2 & 4x
Answers
The like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
What is like terms?Terms whose variables (such as x or y) with any exponents (such as the 2 in x²) are the same are called like terms,
Examples: 7x and 2x are like terms because they are both "x".
Given are some pairs of expressions, we are asked to identify which are like terms,
We know that, according to the definition of the like terms,
Like terms are those terms which contain the same variable which is raised to the same power,
Therefore, the expressions showing the like terms are,
3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
Because, they have same variable with same powers.
Hence, the like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
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question shown below
Answers
The equation of the graphed line can be found to be 2x + 2 y = 4
How to find the equation of the line ?To find the equation of the line, you first need to find the slope which requires picking two points on the line. ( 4, 0 ) and ( 0, 2 )
The slope is:
= Change in y / Change in x
= ( 0 - 2 ) / ( 4 - 0 )
= - 2 / 4
= - 1 / 2
The equation form is:
y = mx + b
m = slope
b = y - intercept which is shown on the line as 2
The equation is:
y = - 1 / 2 x + 2
To put it in the form on the question,
( y = - 1 / 2 x + 2 ) x 2
2 y = - 2 x + 4
2x + 2 y = 4
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