Answer:
14
Step-by-step explanation:
Basically, x is substituted by 10.
So if you plug that into the function, you would get
[tex]f(10)=2(10)-6[/tex]
Simplify it and you get
[tex]f(10)=14[/tex]
model -3/4+5/12 on the number line
The model -3/4+5/12 on the number line is attached in the image below
What is a number line?Generally, A image of a graded straight line is what is known as a number line, and its purpose in elementary mathematics is to serve as a visual representation of real numbers. A number line is the name for this kind of diagram.
It is a widely held belief that a real number may be allocated to each point on a number line, as well as the inverse, which states that a real number can be assigned to each point on a number line.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Find the perimeter of the image below: (4 points)
37 units
38 units
39 units
40 units
38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.
How do you find the perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.
The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }[/tex] ≤ b r/≥ d=[tex]\sqrt{(8-(-2)^{2})+(7-11)^{2} }[/tex] ≤b r/≥
d=[tex]\sqrt{116}[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length:
P = (-2, 11)
T = (8, 7)
The length of PT is [tex]\sqrt{116}[/tex]
The other 4 sides are handled in the same way, and the results are as follows:
TS = [tex]\sqrt{49}[/tex]
SR = [tex]\sqrt{50}[/tex]
RQ = [tex]\sqrt{61}[/tex]
QP = [tex]\sqrt{40}[/tex]
You may calculate the perimeter by adding all the sides:[tex]\sqrt{116}[/tex]+[tex]\sqrt{49}[/tex]+[tex]\sqrt{50}[/tex]+[tex]\sqrt{61}[/tex]+[tex]\sqrt{40}[/tex] = 38.97
The solution is 39 units if you round off.
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If a1=3 and an=-2an-1 then find the whole value of a 5
Answer:
a₅ = 48
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] and a₁ = 3 , then
a₂ = - 2a₁ = - 2(3) = - 6
a₃ = - 2a₂ = - 2(- 6) = 12
a₄ = - 2a₃ = - 2(12) = - 24
a₅ = - 2a₄ = - 2(- 24) = 48
In 2018, the population of Sydney was 5.48 million.
This was 22% of the total population of Australia.
Work out the total population of Australia in 2018
Give your answer correct to 3 significant figures.
The population of Australia in 2018 was 24.909 million.
Given: The population of Sydney in 2018 = 5.48 million
This population of Sydney is equal to 22 % of the total population of Australia.
To find: Total population of Australia
Solution:
According to the Question,
Total population of Australia * 22% = total population of Sydney
Total population of Australia * 22/100 = 5.48 million
= 5.48 million * 100/22
= 24.909 million (approx.)
Hence, the population of Australia in 2018 was 24.909 million.
The total population of Australia in 2018 was 24.90 million.
What is percentage?A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured.
Given that, the population of Sydney was 5.48 million, which was 22% of the total population of Australia.
We need to find the total population of Australia.
Let the total population of Australia be y.
Therefore,
y × 22% = 5.48
y = 5.48 × 100/22
y = 24.90
Hence, the total population of Australia in 2018 was 24.90 million.
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A professor at a large university is interested in determining whether students who have a roommate is associated with the number of hours they are able to study for classes. A simple random sample of 100 students in the university was taken, and each student was asked the following two questions:
1. Do you currently have a roommate?
2. How many hours do you study per week?
The responses of the 100 students are summarized in the frequency table.
Hours Studied Per Week
Roommate Status
Total
No Roommate
One Roommate
Three
15
15
30
Five
20
26
46
More than five
10
14
24
Total
45
55
100
Part A: Calculate the proportion of students in the sample who have a roommate and who study for at least five hours. Also, calculate the proportion of students in the sample who do not have a roommate and who study for at least five hours. (5 points)
Part B: The responses of the 100 students are summarized in the segmented bar graph shown.
A horizontal bar chart is shown with two bars, One Roommate and No Roommate; separated into three sections, Three Hours, Five Hours, More Than Five Hours. Section percentages are for One Roommate, three hours, 27 percent; for One Roommate, five hours, 47 percent; for One Roommate, more than five hours, 26 percent; and for No Roommate, three hours, 33 percent; No Roommate, five hours, 45 percent and for No Roommate, more than five hours, 22 percent.
Write a few sentences summarizing what the graph reveals about the association between roommate status and the amount of hours studied each week among the 100 students in the sample. (5 points) (10 points)
a) The proportion of students at the large university who have a roommate and study for at least five hours is 40%.
b) On average, students with a roommate study for hours more than those with no roommates.
What are proportions and averages?Ratios equated to each other are described as proportions.
Proportion is a part of a whole. Proportions are depicted as decimals, fractions, and percentages.
Average refers to the mean of the data set.
Averages are computed as the quotients of a numerator in relation to a denominator.
Hours Studied Roommate Status Total
Per Week No Roommate One Roommate
Three 15 15 30
Five 20 26 46
More than five 10 14 24
Total 45 55 100
The proportion of students who have a roommate and study for at least five hours = (26+ 14)/100 = 40%
Section Percentages:One Roommate
Three hours 27%
Five hours = 47%
More than five hours = 26%
No Roommate
Three hours 33%
Five hours = 45%
More than five hours = 22%
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The
term-to-term rule for a sequence is given as u_n+1=u_n+2
a) Explain in words what this means.
b)Given that u, = -4, list the first five terms of the sequence.
Answer:
- 8, - 6, - 4, - 2, 0
Step-by-step explanation:
the term- to- term rule
[tex]u_{n+1}[/tex] = [tex]u_{n}[/tex] + 2
means that to find a term in the sequence you add 2 to the previous term.
given u₃ = - 4 , then
u₄ = u₃ + 2 = - 4 + 2 = - 2
u₅ = u₄ + 2 = - 2 + 2 = 0
to find the first 2 terms, rearrange the rule as
[tex]u_{n+1}[/tex] = [tex]u_{n}[/tex] + 2 ( subtract 2 from both sides )
[tex]u_{n+1}[/tex] - 2 = [tex]u_{n}[/tex] , that is
[tex]u_{n}[/tex] = [tex]u_{n+1}[/tex] - 2
this allows for a term to be found by subtracting 2 from the next term, so
a₂ = a₃ - 2 = - 4 - 2 = - 6
a₁ = a₂ - 2 = - 6 - 2 = - 8
the first 5 terms are then : - 8, - 6, - 4, - 2, 0
Write a rule to represent a function for the set of ordered pairs.
Answer:
y = 4[tex]x^{2}[/tex]
Step-by-step explanation:
Your inputs (x's): are -1,0,1,2,3,4 if you plug them into the equation, you get the matching outputs given in the order pairs
input -1 (x value)
y = [tex]4x^{2}[/tex]
y = 4[tex](-1)^{2}[/tex]
y = 4(1)
y = 4
(-1,4)
input 0 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(0)^{2}[/tex]
y 4(0)
y = 0
(0,0)
input 1 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(1)^{2}[/tex]
y = 4(1)
y = 4
(1,4)
input 2 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(2)^{2}[/tex]
y = 4(4)
y = 16
(2,16)
input 3 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(3)^{2}[/tex]
y = 4(9)
y = 36
(3, 36)
input 4 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(4)^{2}[/tex]
y = 4(16)
y = 64
(4,64)
please helppp!!! im confused
There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!
Which statement is true?
A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.
B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25
Using multiplication operation, the TRUE statement about the number of kilograms of dog food in the bag is A. There are approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/25.
How is the number determined?The number of kilograms of dog food in the bag is determined using the multiplication operation.
The multiplication operation is one of the basic mathematical operations, including addition, subtraction, and division.
The multiplication operation involves multiplying the multiplicand by the multiplier to get a result called the product after the equal sign.
The pounds of dog food in a bag = 25 pounds
Approximately 2.2 kilograms = 1 pound
The number of kilograms = 25 x 2.2
= 55 pounds
Thus, Option A is correct since 1/2.2 equals 55/25, based on the multiplication operation.
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Please help with geometry question!!!
Answer:
x = 14EG = 9Step-by-step explanation:
You want the missing length EG and the corresponding value of x in isosceles triangle DEF with midline GH of length 6 parallel to base DF of length 12.
MidlineThe length of segment GH is half the length of segment DF (6/12 = 1/2), so we know that corresponding sides EG and ED have the same ratio:
EG/ED = 1/2
2EG = ED . . . . . . . . . . . . multiply by 2·ED
2(x -5) = (x-5)+9 . . . . . . substitute given values
2x -10 = x +4 . . . . . . . . simplify
x = 14 . . . . . . . . . . . . . add 10-x
Then the length of EG is ...
EG = 14 -5 = 9
I need a so please don,t get it wrong
Answer: 48 square inches
Step-by-step explanation:
To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.
area of triangle L x W = 6x4=24
area of rectangle LxW =6x4=24
24+24=48
10. When cycling 2.4km to the beach, the wheels on Sue's bike
rotated 1255 times. Find the diameter of the wheels.
Therefore , the solution of the given problem of circle comes out to be
the diameter is 62 cm.
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.
Here,
Given : Sue covered 2.4 km distance and
bike wheel rotated 1225 times.
Thus,
To find the value of diameter of the wheel
=>2400=2πr*1225
=> 2400/2 = πr*1225
=> 1200 = πr*1225
=>r=31
Diameter = 2*31 = 62cm
Therefore , the solution of the given problem of circle comes out to be
the diameter is 62 cm.
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One aircraft has a capacity of 64 more seats than a second
aircraft. A third aircraft has 152 seats less than twice the seating
capacity of the second aircraft. If their total number of seats is
1900, find the number of seats for each aircraft.
Therefore, the number of seats for each aircraft is 752, 688, and 1224.
Define Unitary method.The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
Let x be the number of seats for the second aircraft.
The first aircraft has x + 64 seats.
The third aircraft has 2x - 152 seats.
The total number of seats for all aircraft is x + (x + 64) + (2x - 152) = 1900.
Therefore, 3x = 2064, so x = 688.
The first aircraft has 688 + 64 = 752 seats.
The third aircraft has 2(688) - 152 = 1224 seats.
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Jason likes to play video games. His parents allow him to play for 20 min plus 10
min for each half hour he does chores or studies. He can never play for more
than 90 min/day.
The function f(x)=20+10x models the number of minutes per day Jason could
play where x represents the number of half hour increments he has done chores
or studied.
What is the practical range of the function?
A. all multiples of 10 greater than or equal to 20 and less than or equal to 90
B. all integers
C. all real numbers greater than or equal to 20
D. all real numbers
Answer:all integers
Step-by-step explanation:
the correct is all integers
How would you solve questions 25a+b?
Answer:
(a) See attachment.
(b) 12:23
Step-by-step explanation:
Part (a)A bearing is the angle (in degrees) measured clockwise from north.
To mark the position of J on the given map:
Measure an angle of 36° clockwise from K and draw a line.Measure an angle of 284° clockwise from L and draw a line.The location of J is the point of intersection of the two lines.(See attachment).
Part (b)Given:
Distance between K and L = 9600 mSpeed Kendra walks from K to L = 4.5 km/hConvert 9600 meters into kilometers by dividing by 1000:
⇒ 9600 m = 9600 ÷ 1000 = 9.6 km
[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Therefore:
[tex]\sf Time=\dfrac{Distance}{Speed}[/tex]
Substitute the given distance and speed into the formula to calculate the time it took Kendra to walk from K to L:
[tex]\implies \sf Time=\dfrac{9.6\;km}{4.5\;km/h}=2.133333...\;hours[/tex]
Convert 2.133333.. into a mixed number:
[tex]\implies \sf 2.133333...=2\frac{2}{15}\;hours[/tex]
To find the number of minutes in 2/15ths of an hour, multiply 2/15 by 60:
[tex]\implies \sf \dfrac{2}{15} \times 60=\dfrac{120}{15}=8\;minutes[/tex]
Therefore, it took Kendra 2 hours and 8 minutes to walk from K to L.
If Kendra left at 10:15:
[tex]\implies \sf 10:15 + 2\;hours = 12:15[/tex]
[tex]\implies \sf 12:15 + 8\;minutes=12:23[/tex]
Therefore, Kendra arrived at L at 12:23.
HELP PLS
Factor the trinomal or stage that the trinomal is prime
The correct answer is x² - 7x - 18 = (x - 9)(x + 2)
These points are linear. Find the slope.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }[/tex]
devin has a ribbin that is 2 ft long. he cuts it into peices, s shown in the model
The model shows that there are 10 pieces that are each 0. 2 ft long.
How to find the number of pieces ?From the given model, we see that Devin cut the ribbon in equal proportions. The number of proportions can be found by summing the different sections on the ribbon.
This number comes to 10 sections which means that Devin cut the ribbon into 10 pieces.
The length of each of these pieces is:
= Length of entire ribbon / Number of pieces
= 2 / 10
= 0. 2 ft long
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"Customers of CC Car Wash visit the station at a constant rate (you can ignore any effects of variability) of 40 customers per day. Of these customers, 40 percent buy Package 1, 15 percent buy Package 2, 15 percent buy Package 3, and 30 percent buy Package 4. The mix does not change over the course of the day. The store operates 12 hours a day."
According to the information, we can infer that the number of customers that buy package 1 is 16 customers.
How to calculate how many customers buy package 1?To calculate how many customers buy package 1 we have to identify some important information such as:
Total customers: 40 customers.Percent that buy package 1: 40%To calculate this value, we have to divide 40 in 100, and then we have to multiply the result by 40.
40 / 100 = 0.40.4 * 40 = 16According to previous information, the number of customers that buy package 1 is 16 customers. So, 24 customers buy package 2, 3 or 4. If we have to identify exactly how many buy an specific package we have to make the same procedure. For example package 3.
40 / 100 = 0.4
0.4 * 15 = 6
So, 6 customers buy package 3.
Note: This question is incomplete because there is some information missing. Here is the complete information:
TASK
Calculate how many customers buy package 1.
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Make sure to show working
Hope it helps. If you have any query, feel free to ask.
Your business requests a 3-month loan for
$450,000. What will be the interest paid at the
end of the term if the business risk percentage is
assessed at 2.0% and LIBOR is at 2.8%?
interest paid = $ [?]
Round to the nearest hundredth.
Enter
PH
Skip
The interest paid at the term end will be $5400.
What is interest and its types(Simple and compound interest)?
Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.
The formula for these are
Simple Interest= P×r×n
where:
P=Principal amount
r=Annual interest rate
n=Term of loan, in years
Compound Interest=P×(1+r)^t−P
where:
P=Principal amount
r=Annual interest rate
t=Number of years interest is applied
Here,
Interest rate will be risk percentage + LIBOR
i.e.4.8%
Hence, the interest can be found by using formula for simple interest
Therefore,
SI=P*r*t
=$450000*0.048*0.25 (Time is 3 month or 0.25 years.)
SI (Interest paid)=$5400
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The interest paid at the end of the 3-month loan term for a loan amount of $450,000 with a business risk percentage of 2.0% and a LIBOR rate of 2.8% would be $5,040.
What is interest and step by step explanation for given question?Interest is the cost of borrowing money, typically a percentage of the loan amount. It is paid by the borrower to the lender in addition to the principal of the loan. Interest rates can vary depending on factors such as creditworthiness and market conditions.The interest paid can be calculated by using the formula:Interest = Principal x (Business Risk Percentage + LIBOR Rate) x (Number of months / 12)Therefore, in this case:Interest = $450,000 x (2.0% + 2.8%) x (3/12)Interest = $450,000 x 5.0% x 0.25Interest = $5,625Rounded to the nearest hundredth, the interest paid would be $5,040.To learn more about interest refer:
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hello , please help !
Answer:
4,7
Step-by-step explanation:
4,7
A,B,C,E,F et G sont du plan Simplifier l’écriture de chacun des sommes 1)AB+CE+BC+EF 2) AB+DE+AB+EG 3) AB-BC-AB+BE 4) AB+DE+CD+AD+BC+ED
1.5 (-2)^(n-1) > -6000
Find n (n is integer)
Answer:
что там а? я даже не знаю hehe
5, Infigure 4.48 • vertical cliff IS Hom high and is absor ved from about which is from from the foot of the cliff calculate the angle of elevation of the top of the cliff from boak ?
Therefore , the solution of the given problem of elevation comes out to be
X = 21.23°.
What is the elevation and depression angle?When it is between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.
Here,
Given : tan X = P/ B
tan X = 68 / 175
X = tan⁻¹ (68 /175)
X = 21.23
Therefore , the solution of the given problem of elevation comes out to be
X = 21.23°.
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Please help me with this
Answer:
A represents f(x) and B represents g(x)
Step-by-step explanation:
choose a value for x, substitute , say x = 1 into both f(x) and g(x) , then check the values obtained on the graph.
f(x) = 100 × [tex](\frac{3}{5}) ^{1}[/tex] = 100 × [tex]\frac{3}{5}[/tex] = 20 × 3 = 60
thus (1, 60 ) is a point on the graph of f(x)
the point (1, 60 ) is on graph A
g(x) = 100 × [tex](\frac{2}{5}) ^{1}[/tex] = 100 × [tex]\frac{2}{5}[/tex] = 20 × 2 = 40
thus (1, 40 ) is a point on the graph of g(x)
the point (1, 40 ) is on graph B
5) Is the sequence geometric?
a) 100, 25, 6.25, 1.5625,....
b) 3, -8, -19, -30,...
The sequence of 100, 25, 6.25, 1.5625 is geometric.
What is meant by geometric?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.
In essence, we multiply the numbers together and calculate their n[tex]th[/tex]root, where n is the total number of data values.
A succession of shapes are used to create geometric patterns.
Because the pattern is governed by a rule, patterns created from shapes are comparable to patterns created from numbers.
The dimensions, perimeter, area, surface area, volume, etc. of geometric shapes are determined using geometry formulas.
Mathematics' branch of geometry examines the connections between points, lines, angles, surfaces, solids' measurements, and qualities.
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Inso ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, how many gallons of ice cream can 4
machines make?
The gallons of ice cream 4 machines can make is 650 gallons.
How to find the number of gallons of ice cream 4 machine can make?Two ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:
Therefore,
If 2 ice cream machine = 320 gallons
4 ice cream machine = ?
cross multiply
Hence,
gallons of ice cream made by 4 machines = 320 × 4 / 2
gallons of ice cream made by 4 machines = 1280 / 2\
Therefore,
gallons of ice cream made by 4 machines = 640 gallons
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Please help me solve this i'm not sure what else to do
The equation of the line in point-slope form is obtained as y = -2x + 4.
What is the point-slope form?
Point-slope is the general form of a linear equation which is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
The line passes through point (x1,y1) = (0,4)
The slope of the line is m = -2.
The formula for point-slope form of equation is -
y-y1=m(x-x1)
Substituting the values in the equation -
y - 4 = -2(x - 0)
y - 4 = -2x
y = -2x + 4
Therefore, the equation is obtained as y = -2x + 4.
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