The expected number (μ) of property crimes that will be solved in this district can be found by multiplying the total number of property crimes by the probability that a property crime will be solved. Since the probability that a property crime will be solved is 1 - 0.84 = 0.16, the expected number of property crimes that will be solved is:
μ = 7 × 0.16 = 1.12
The standard deviation (σ) of this distribution can be found by taking the square root of the product of the total number of property crimes, the probability that a property crime will be solved, and the probability that a property crime will not be solved:
σ = √(7 × 0.16 × 0.84) = 1.01
Therefore, the expected number of property crimes that will be solved in this district is 1.12, and the standard deviation of this distribution is 1.01.
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QUESTION: LetP=[72753231]. Answer the following: 1. (1 mark) Explain (briefly) whyPis a regular transition matrix. 2. (2 marks) Given the initial state vectorx0=[103107]T, find the state vectorx2. 3. (3 marks) Calculate the steady state vector. SHOW YOUR WORK!
1. A transition matrix is regular if there is a positive integer k such that P^k has all positive elements.
2. The value of x2 = [128,295, 44,557]T.
3. The value of x = [0.701, 0.299, 0]T .
1. P is a regular transition matrix because it has all positive elements, meaning that it is possible for any state to transition to any other state.
2. To find the state vector x2, we need to multiply the initial state vector x0 by the transition matrix P twice:
x2 = P^2 * x0
= P * P * x0
= P * [72 * 10 + 75 * 7, 32 * 10 + 31 * 7]T
= P * [945, 457]T
= [72 * 945 + 75 * 457, 32 * 945 + 31 * 457]T
= [128,295, 44,557]T
3. To find the steady state vector, we need to solve the equation Px = x for x. This means that we need to find the eigenvector of P corresponding to the eigenvalue
1. We can do this by finding the null space of (P - I), where I is the identity matrix:
(P - I)x = 0
=> [71 -75 0, -32 30 0, 0 0 -1]x = 0
=> x = c[75, 32, 0]T, where c is a constant.
To find the steady state vector, we need to normalize this eigenvector so that it sums to 1:
x = [75/107, 32/107, 0]T
= [0.701, 0.299, 0]T
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if a poisson process rate was 1.5 (15 events in 10 min) with a mean of 0.387, then solve the following
a) p(no events for 3 min)
b) p(1 event in 1 min)
c) p(>= 1 event in 1 min)
d) uncertainty for a, b, c
If a poisson process rate was 1.5 (15 events in 10 min) with a mean of 0.387, then
a) p(no events for 3 min) - 0.0498
b) p(1 event in 1 min) - 0.3347
c) p(>= 1 event in 1 min) - 0.7769
d) uncertainty for a, b, c - For a), σ = 1.732 and for b) and c), σ = 1.225
A Poisson process is a stochastic process that counts the number of events in a given time interval. It is characterized by two parameters: the rate, λ, which is the average number of events in a given time interval, and the mean, μ, which is the average number of events in the entire process.
a) The probability of no events in 3 minutes is given by the Poisson probability mass function:
P(X = 0) = (λt)^0 * e^(-λt) / 0! = e^(-λt)
Where t is the time interval (3 minutes), and λ is the rate (1.5 events per minute). Plugging in the values gives:
P(X = 0) = e^(-1.5 * 3) = 0.0498
b) The probability of 1 event in 1 minute is given by the Poisson probability mass function:
P(X = 1) = (λt)^1 * e^(-λt) / 1! = λt * e^(-λt)
Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:
P(X = 1) = 1.5 * e^(-1.5) = 0.3347
c) The probability of at least 1 event in 1 minute is given by the complement of the probability of no events:
P(X >= 1) = 1 - P(X = 0) = 1 - e^(-λt)
Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:
P(X >= 1) = 1 - e^(-1.5) = 0.7769
d) The uncertainty for each of the probabilities is given by the standard deviation of the Poisson distribution:
σ = sqrt(λt)
For a), the standard deviation is:
σ = sqrt(1.5 * 3) = 1.732
For b) and c), the standard deviation is:
σ = sqrt(1.5 * 1) = 1.225
Therefore, the uncertainty for each of the probabilities is given by the standard deviation.
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A grocery store receives a 180-pound crate containing six 10-pound bags of potatoes and an ink own number of 5 pound bag of potatoes. How many 5 pound bags of potatoes are in the crate
There are 24 five-pound bags of potatoes in the crate.
The crate contains a total of 6 bags of potatoes weighing 10 pounds each, which is a total of 60 pounds.
So, the remaining weight of the crate is 180 pounds - 60 pounds = 120 pounds.
Let's assume that there are x five-pound bags of potatoes in the crate.
Therefore, the total weight of these x bags of potatoes would be 5x pounds.
We know that the weight of the entire crate is 180 pounds,
60 pounds (weight of 6 bags of 10-pound potatoes) + 5x pounds (weight of x 5-pound bags of potatoes) = 180 pounds (weight of the entire crate)
60 + 5x = 180
5x = 180 - 60
5x = 120
x = 24
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To get the 10% discount, a shopper must spend at least $500.
Use d to represent the spending (in dollars) of a shopper who gets the discount.
The cruising speed of the bullet train will be no less than 130 miles per hour.
Use s to represent the train's cruising speed (in miles per hour).
Answer:
d>500
t>130
Step-by-step explanation:
For the first problem:
we must set up an inequality to answer :D soooo:
d>500
the same thing goes for the second one:
t>130
Hope this is right!
Express the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form.
The product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).
To express the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form, we need to multiply the two binomials using the distributive property.
First, we will multiply the first term of the first binomial by each term of the second binomial:
(2/3)x * 2x = (4/3)x^2
(2/3)x * (5/6) = (10/18)x = (5/9)x
Next, we will multiply the second term of the first binomial by each term of the second binomial:
(4/3) * 2x = (8/3)x
(4/3) * (5/6) = (20/18) = (10/9)
Now we will combine like terms:
(4/3)x^2 + (5/9)x + (8/3)x + (10/9) = (4/3)x^2 + (13/9)x + (10/9)
Therefore, the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).
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Order the values from least to greatest. |-41, 10, -12, 13| A) -41, 131, 10, -12 O B) |3|, |-–4|, 10, −12 OC -12, 1-41, [3], 10 OD) -12, 131, |–4], 10 D
The order of the number from least to greatest will be -12, |3|, |-4|, 10. Then the correct option is D.
What is ascending order?It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.
The numbers are given below.
|-4|, 10, -12, |3|
Determine the absolute value of the numbers, then we have
|-4| = 4
10 = 10
-12 = -12
|3| = 3
The order of the number from least to greatest will be given as,
-12, 3, 4, 10
-12, |3|, |-4|, 10
Thus, the correct option is D.
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Gary and Greg share a 30-ounce box of cereal. By the end of the week, Gary has eaten 3/10 of the box, and Greg has eaten 3/5 of the box of cereal. How many ounces are left in the box?
Answer:
3
Step-by-step explanation:
cuz ik
What is the volume of a rectangular prism with a length of 4.7 feet, a width of 1.5 feet, and a height of 1.6 feet?
Responses
7.1 ft³
7.1 ft³
7.8 ft³
7.8 ft³
8.65 ft³
8.65 ft³
11.28 ft³
The volume of the rectangular prism is 11.28 feet³.
What is a rectangular prism?In terms of geometry, a rectangular prism is a polyhedron having two parallel, congruent bases. It also goes by the name cuboid. A rectangular prism is made up of six rectangles, each with twelve edges.
We are given that a rectangular prism has the following dimensions:
Length (l) = 4.7 feet
Width (w) = 1.5 feet
Height (h) = 1.6 feet
We know that
Volume (V) = [tex]l \times w \times h[/tex]
From this, we get
⇒V = [tex]4.7 \times 1.5 \times 1.6[/tex]
⇒V = 11.28 feet³
Hence, the volume of the rectangular prism is 11.28 feet³.
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Answer: Your answer is 11.28 ft³
Step-by-step explanation: 4.7 x 1.5 x 1.6 = 11.28 you have to do it in this order also I did the k12 quiz here's proof.
Hope it helped :D
Mei and Ming both improved their yards by planting rose bushes and ivy they bought their supplies from the same store Mei spent 36 on 3 rose bushes and 1 pot of ivy Ming spent 168 on 9 rose bushes and 8 pots of ivy what's the cost of one rose bush and one pot of ivy..
The cost of one rose shrub costs $12 and one pot of ivy costs $24, respectively.
How can you theoretically solve an equation system?It takes two equations with two variables to solve a system of equations. The variables can then be solved for using algebraic techniques like substitution or elimination.
Let x be the cost of one rose bush and y be the cost of one pot of ivy.
From Mei's purchase, we have:
3x + y = 36
From Ming's purchase, we have:
9x + 8y = 168
Use the first equation to solve for y:
y = 36 - 3x
Substituting this into the second equation, we get:
9x + 8(36 - 3x) = 168
9x + 288 - 24x = 168
-15x = -120
x = 8
Substituting x = 8 into equation of y, we get:
y = 24
Hence, the cost of one rose bush is $8, and the cost of one pot of ivy is $24.
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Jack,Sam and pandu wrote three different Maths test on Monday. Jack got 5 out of 10 for his test. Sam got 22 out of 40 for his test, and pandu got 12 out of 20. By converting the fractions into percentages , determine who achieved the best score
Among Jack, Pandu and Sam, Pandu scored the best as his marks scored percentage is 60%.
What is percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'.
Solution according to the information given:
Jack's percentage = (5/10)×100
= 50%
Sam's percentage = (22/40)×100
= (11/20)×100
= 55%
Pandu's percentage = (12/20)×100
= 60%
Thus, Pandu scored the best marks by scoring 60%.
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What are the other three angle measures if ∠1 has a measure of 45°?
The measures ∠2 = 135°, ∠5 = 45°, ∠6 = 135°, ∠4 = 45° and ∠3 = 135°.
What are Angles?An angle is formed when two straight lines or rays meet at a common endpoint.
The angle ∠1 = 45° is given.
Types of the angles are as follows;
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Alternate angle - If two lines are parallel then the third line will make z -angle and z-angles are equal angles with the parallel lines.
∠1 + ∠2 = 180° (Supplementary angle)
45° + ∠2 = 180°
∠2 = 135°
∠1 = ∠5 = 45° (Corresponding angle)
∠2= ∠6 = 135°
∠4 = 45° (Alternate angle)
∠3 = 135° (Alternate angle)
Hence, the measures ∠2 = 135°, ∠5 = 45°, ∠6 = 135°, ∠4 = 45° and ∠3 = 135°.
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A swimming camp charges $190 for 6 weeks of swimming lessons and $265 for 9 weeks of swimming lessons. How much does the swimming camp charge per week?
The camp charge per week = slope = $25 per week.
How to Apply the Slope Concept?The slope is also referred to as the unit rate which is given as: m = change in y / change in x.
From the given scenario, let:
x = number of weeks
y = camp charges
We will therefore have these two points:
(6, 190) and (9, 265)
Use the two points to find the slope, which is the swimming camp charge per week:
Camp charge per week (m) = change in y / change in x = 265 - 190 / 9 - 6
= 75/3
= $25 per week.
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The expression 4x + 13 represents the time it takes a commuter to travel in the morning to work. The expression 10x – 2 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
14x + 15
14x + 11
6x + 11
6x + 15
Answer:
The total travel time is the sum of the time it takes to travel in the morning and the time it takes to travel in the evening.
Total travel time = (morning travel time) + (evening travel time)
= (4x + 13) + (10x - 2)
= 14x + 11
Therefore, the total travel time is 14x + 11. Answer: B.
Answer:
B: 14x+11
Step-by-step explanation:
i took the test and got it right
2) How many widgets (to the nearest tenth) can be produced by 360 workers in 20 hours?
Assuming a constant rate of production, 360 workers can produce approximately 7200 widgets in 20 hours.
The problem asks how many widgets can be produced by 360 workers in 20 hours. To solve this problem, we need to use the formula:
widgets = rate x time x workers
We know the time is 20 hours and the number of workers is 360. We need to find the rate at which the workers can produce widgets. Let's assume that each worker can produce one widget in one hour, so the rate is 1 widget per worker-hour.
Substituting the values, we get:
widgets = 1 x 20 x 360
widgets = 7200
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I need some help with b) and c)
The volume of the oblique cone is 5887.5 ft³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
We know, The volume of an oblique cone is, (1/3)×B×h.
Where h = height and B = area of the base.
Here the area of the base is, π(15)² = 706.5 ft², and the height is 25 feet.
Therefore, The volume is,
= (1/3)×706.5×25.
= 5887.5 ft³
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100 POINTS PLEASEEE SOMEBODY I NEED TO TURN THIS IN
The diagonals are 17.4 inches
The length does not meet the regulationThe measurement of KR is 8 unitsHow to determine the lengths of the diagonalsFrom the question, we have the following parameters that can be used in our computation:
DH = 10, HK = 8.2, KB = 6, HR = 8 and KY = 6.8
Given that DHB is a right triangle, we have
DB² = HB² + DH²
So, we have
DB² = (8.2 + 6)² + 10²
DB² = 301.64
Take the square root
DB = 17.4
Does the length meet the regulationThe triangles DBY and RYB are congruent triangles
So, we have
RY = 17.4
The figure is an isosceles triangle, and the length does not meet the regulation
This is so because the length is less than the required 20 inches
The measurement of KRThe two non-parallel sides of an isosceles triangle are of equal length
So, we have
1/2x + 5 = 2x - 4
Evaluate the like terms
3/2x = 9
This gives
x = 9 * 2/3
x = 6
So, we have
KR = 1/2x + 5
This gives
KR = 1/2 * 6 + 5
KR = 8
So, the value of KR is 8 units
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Dina Lincoln purchases a $1,299.99 treadmill, a $52.99 treadmill mat and 2 pairs of running shorts at
$24.99 each. The state sales tax rate is 6.25% and the county tax rate is 1.5%. What is the sales tax on
her purchases?
A)$108.73
B)$106.79
C)$103.35
D) $98.21
Answer:108.73
Step-by-step explanation: To get the total sales tax you add box of the taxes together wich gives you 7.75%, then you find the total amount of money he spent, which was 1402.96. Lastly you find 7.75% of 1402.96 which is 108.73
Nina has 100 rupess note. She spent 40 rupess on clothes so she is left with 60 rupees then she spent 30 rupees on food so she is left with with 30 rupess and now she spends 18 rupess on jewellry so she is left with 12 rupees then she spends 12 rupess on snacks and now she is left with 0 rupess. Now when she adds 40, 30, 18, 12 she gets 100 rupees but when she adds 60, 30, 12 and 0 she gets 102. How?
given f(x)=x+2 setting k=4 affects the slope and y- intercept of the graph of g compared to the graph of f g(x) = 4(x + 2)
The constant term is 8, which means that the y-intercept of the graph of g is (0, 8).
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in a set. It is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. Functions are widely used in various fields of mathematics, science, engineering, and technology to model and analyze real-world situations, to describe how quantities depend on one another, and to solve problems.
Here,
If we set k=4, the function g(x) becomes:
g(x) = k(x+2) = 4(x+2)
The value of k affects the slope of the graph of g compared to the graph of f. In this case, since k=4, the slope of the graph of g is 4 times the slope of the graph of f.
The slope of the graph of f is 1, since the coefficient of x is 1. Therefore, the slope of the graph of g is:
4 * 1 = 4
This means that the graph of g is steeper than the graph of f.
The y-intercept of the graph of f is 2, since the constant term is 2. Setting k=4 does not affect the y-intercept of the graph of g, since the constant term remains the same:
g(x) = 4(x+2) = 4x + 8
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La diferencia "8 menos que q
Answer:
q - 8
Step-by-step explanation:
q - 8
Answer:
q=0
Step-by-step explanation:
Express bar (xY) in component form. Then aph bar (xY). x=[[-9],[10]] and Y=[[-4],[3]]
The component form of bar (xY) = [[36],[30]] and aph bar (xY) = [[36, 30]]
To express bar (xY) in component form, we need to multiply the matrices x and Y together. The result will be a 2x1 matrix, which is the component form of bar (xY).
First, we multiply the first row of x by the first column of Y:
[-9] * [-4] = 36
Next, we multiply the second row of x by the second column of Y:
[10] * [3] = 30
Now we can put these two results together to get the component form of bar (xY):
bar (xY) = [[36],[30]]
To aph bar (xY), we simply take the transpose of the matrix. This means that we switch the rows and columns:
aph bar (xY) = [[36, 30]]
So the final answer is:
bar (xY) = [[36],[30]]
aph bar (xY) = [[36, 30]]
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The perimeter of the rectangle below is 80 units. Find the length of side CD.
Write your answer without variables.
D
4z + 2
C
3z + 3
B
CD
The required length of side CD is 22 units.
How to use perimeter to solve for variable?Since the perimeter of the rectangle is 80 units, we can use the formula for the perimeter of a rectangle, which is:
perimeter = 2(length + width)
In this case, we know that the perimeter is 80 units, so we can write:
80 = 2(length + width)
We also know that CD is a side of the rectangle, so it must be either the length or the width. Let's assume that CD is the length, so we can write:
CD = 4z + 2
Substituting this expression for the length into the formula for the perimeter, we get:
80 = 2(4z + 2 + width)
Simplifying the right-hand side, we get:
80 = 8z + 4 + 2width
Subtracting 4 from both sides, we get:
76 = 8z + 2width
Dividing both sides by 2, we get:
38 = 4z + width
Now we can use the fact that CD is a side of the rectangle to substitute for width. Since the opposite side of the rectangle must also have length 4z + 2, we can write:
width = 3z + 3
Substituting this into the previous equation, we get:
38 = 4z + 3z + 3
Simplifying the right-hand side, we get:
38 = 7z + 3
Subtracting 3 from both sides, we get:
35 = 7z
Dividing both sides by 7, we get:
5 = z
Now we can substitute this value of z into the expression for CD:
CD = 4z + 2 = 4(5) + 2 = 22
Therefore, the length of side CD is 22 units.
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Answer the next 4 questions
12) if the base area of a square prism is 15 square centimeters and the hight is eight centimeters, what is the volume of the prism?
13) if the base area of a square prism is 16 sq cm and the height is 20 centimeters, what is the volume of the prism?
14) if the base area of a cylinder is 15.6 square centimeters and the height is four centimeters, what is the volume of the cylinder?
15) if the base area of a cylinder is 1.2 square centimeters and the height is three centimeters, what is the volume of the cylinder?
Answer:
I don't know dude...............
Determinants: Let A∈R n×n be an invertible matrix, and letdet(⋅)denote the determinant of its argument. Show thatdet(A−1)=det(A)1
The determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix.
Determinants: The determinant of an invertible matrix A is a scalar value that is used to indicate the invertibility of the matrix. If the determinant of A is non-zero, then the matrix is invertible. The determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix. In other words, det(A−1)=det(A)1.
To prove this, we can use the property of determinants that det(AB)=det(A)det(B) for any two square matrices A and B. Since A is an invertible matrix, we know that AA−1=I, where I is the identity matrix. Taking the determinant of both sides of this equation gives us:
det(AA−1)=det(I)
Using the property of determinants mentioned above, we can rewrite the left-hand side of the equation as:
det(A)det(A−1)=det(I)
Since the determinant of the identity matrix is 1, we can simplify the equation to:
det(A)det(A−1)=1
Dividing both sides of the equation by det(A) gives us:
det(A−1)=det(A)1
Therefore, the determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix.
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what is 2divided by 80000000
40000000
Step-by-step explanation:
ezy Peasy lemon squeeze
Answer:40,000,000
Step-by-step explanation:
its just like 2 divided by 8 which is 4 then just add all your zeros
Help the teacher told me to solve them and shade them
The graph and the solution to the system of inequalities are added as attachments
How to determine the solution to the system of inequalitiesSystem 1
From the question, we have the following parameters that can be usedin our computation:
x ≤ -3
y < 5/3x + 2
The above system is a system of inequalities that contain two linear inequalities
Next, we plot the graph
One of the points in the shaded region is (-4, -5)
System 2
Here, we have the following system
y ≤ -5/2x - 2
y < -1/2x + 2
The above system is a system of inequalities that contain two linear inequalities
Next, we plot the graph
One of the points in the shaded region is also (-4, -5)
System 3
Here, we have the following system
y ≥ 2/3x + 3
y > -4/3x - 3
The above system is a system of inequalities that contain two linear inequalities
Next, we plot the graph
One of the points in the shaded region is also (4, 7)
See attachment for the graph of the inequalities
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Rearrange the equation 4y - 8 = 12x + 4 into slope intercept form
Answer:
[tex]x = \frac{y}{3} - 1[/tex]
Step-by-step explanation:
[tex]1. \: 4y - 8 - 4 = 12x \\ 2. \: 4y - 12 = 12x \\ 3. \: \frac{4y - 12}{12} = x \\ 4. \: \frac{4(y - 3)}{12} = x \\ 5. \: \frac{y - 3}{3} = x \\ 6. \: - 1 + \frac{y}{3} = x \\ 7. \: \frac{y}{3} -1 = x \\ 8. \: x = \frac{y}{3}-1[/tex]
7. Find the measure of 2
35°
5
2
1
3
The measure of the 2 angle in the triangle is 55 degrees.
What is kite ?In geometry, a kite is a quadrilateral with two pairs of adjacent sides that are equal in length. This means that a kite is a special type of quadrilateral called a "tangential quadrilateral" because its sides can be inscribed in a circle.
According to given information:If one angle of a triangle is a right angle (90 degrees) and another angle is 35 degrees, then the sum of the three angles in the triangle is 180 degrees.
Therefore, the measure of the third angle can be found by subtracting the sum of the other two angles from 180 degrees:
Third angle = 180 degrees - 90 degrees - 35 degrees
Third angle = 55 degrees
So the measure of the 2 angle in the triangle is 55 degrees.
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How many 5/8's are in 1? Its supposed to be a mixed number (ex, 1 1/3)
There are 1 and 3/5 of 5/8 in 1, if Its supposed to be a mixed number.
What is a mixed number?
A mixed number is a combination of a whole number and a fraction. It is written in the form of "a b/c" where a is the whole number, b is the numerator of the fraction, and c is the denominator of the fraction.
To answer your second question, we can divide 1 by 5/8 as follows:
1 ÷ 5/8 = (1 x 8) ÷ 5 = 8/5
We can then write 8/5 as a mixed number by dividing the numerator (8) by the denominator (5) and writing the remainder as the fraction part.
8 ÷ 5 = 1 with a remainder of 3, so we write the answer as:
1 3/5
Therefore, there are 1 and 3/5 of 5/8 in 1.
To learn more about the mixed number, visit:
https://brainly.com/question/414559
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need help with this problem
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-2)}) \implies y +4= \cfrac{1}{2} (x +2) \\\\\\ y+4=\cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x-3 \end{array}}[/tex]