Both Samuel and Helena are correct as the slope-intercept form and the point-slope form can be used to find the equation of a line given two points. The slope-intercept form is y = mx + b, while the point-slope form is y - y1 = m(x - x1). The methods vary but both are effective depending on the given information.
Explanation:Both Samuel and Helena are correct; they have mentioned different forms that can be used to find the equation of a line given two points. The slope-intercept form of a linear equation is commonly written as y = mx + b, where m represents the slope and b represents the y-intercept. The slope, m, describes the steepness of the line, and the y-intercept, b, is where the line crosses the y-axis. In contrast, the point-slope form is written as y - y1 = m(x - x1), where (x1, y1) is a specific point on the line and m is the slope. To find the slope, you take two points on the line, say, (x1, y1) and (x2, y2), and use the formula m = (y2 - y1)/(x2 - x1).
Either form will produce the equation of the line, but they require different approaches. The slope-intercept form immediately gives the y-intercept and is generally used when this information is valuable or when the graph will be drawn. Meanwhile, the point-slope form is particularly handy when you have one point on the line and the slope, as it can be used quickly without re-arranging the equation to solve for the y-intercept.
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Both Samuel and Helena's methods are valid for finding the equation of a line. The slope-intercept form (y = mx + b) requires finding the y-intercept, while the point-slope form (y - y1) = m(x - x1) uses a point on the line directly. Both forms yield the same final equation.
Both Samuel and Helena are correct, but they are using different methods to find the equation of a line. The slope-intercept form and the point-slope form can both lead to the same final equation of the line, which will be consistent after simplifying. Here's a step-by-step explanation of both forms:
Slope-Intercept Form (y = mx + b)Slope-Intercept Form is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
First, find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).Next, use one of the given points (x1, y1) and substitute in the found slope and coordinates to solve for b (the y-intercept).Substitute the slope and y-intercept back into the slope-intercept form.Example:
Given points (1, 2) and (3, 4):
Calculate the slope: m = (4 - 2) / (3 - 1) = 2 / 2 = 1.Use one of the points to find b: 2 = 1(1) + b; solving this, we get b = 1.Equation of the line: y = 1x + 1.Point-Slope Form (y - y1) = m(x - x1)The Point-Slope Form is given by the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
First, find the slope (m) using the same formula: m = (y2 - y1) / (x2 - x1).Use one of the given points (x1, y1) and substitute in the found slope.Simplify the equation to convert it to slope-intercept form if needed.Example:
Given points (1, 2) and (3, 4):
Calculate the slope: m = (4 - 2) / (3 - 1) = 2 / 2 = 1.Select point (1, 2): y - 2 = 1(x - 1).Simplify: y - 2 = x - 1;y = x + 1.
Both forms ultimately lead to the same linear equation. Choosing which form to use depends on what information is given and personal preference.
a newspaper has 80 Pages if 20 of the 80 pages are devoted to advertising what percent of the newspaper is advertising
Two students, Ann and Max, factored the trinomial 4x2 − 6x − 4. Ann factored it as 2(x − 2)(2x + 1) and Max factored it as (x − 2)(4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why.
We want to partition 100 mL into 10 equal parts. ow many milliliters should we pour in each cup?
If we want to divide 100 mL into 10 equal parts we have to pour 10 mL into each cup.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
It is given that we want to divide 100 mL into 10 equal parts,
Suppose x milliliters should we pour into each cup,
x = Total volume / Number of cups
x = 100 mL / 10
x =10 mL
Thus, if we want to divide 100 mL into 10 equal parts we have to pour 10 mL into each cup.
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the sum of four times a number and seven is ten
The unknown number is = 3/4
Let the unknown number be X
4(X) + 7 = 10
Minus 7 from the both sides:
4x +7 -7 = 10 -7
4x + 0 = 3
4x = 3
Make x the subject of formula by dividing both sides by 4,
4x/4 = 3/4
Therefore,
x= 3/4
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Amultivitamin tablet contains 16.5 mg calcium.How much calcuim does a bottle of 20 tablet contain?
The opposite of three times a number is more than 48. What are the possible values of the missing number
Can someone solve this fast , for 20 points
Kendra and her horse completed barrel racing course in 15.839 seconds what is the number rounded to the nearest tenth
Answer:
The number rounded to the nearest tenth is 15.8.
Step-by-step explanation:
Kendra and her horse completed barrel racing course in 15.839 seconds.
So, the number rounded to the nearest tenth or 0.1 is 15.8 because the number next to 8 is 3, it will not make eight '9' .
Hence, the number rounded to the nearest tenth is 15.8.
Round 12,909 to the nearest hundreds
Write a multiplication problem using two 2 digit factors with a resulting product that falls between 7,000 and 8,000
The multiplication problem using 2-digit factors with a resulting product that falls between 7,000 and 8,000 is 81x90 = 7290.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that:
The number are 7,000 and 8,000
Let A and B be the two-digit number with a resulting product that falls between 7,000 and 8,000:
Let two numbers are:
81 and 90
The product of the numbers:
81x90 = 7290
The product of number falls between 7,000 and 8,000.
Thus, the multiplication problem using 2-digit factors with a resulting product that falls between 7,000 and 8,000 is 81x90 = 7290.
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How long would it tak a bus traveling 50 km/h to travel 125 km?
Answer: It will take the bus 2.5 hours to travel 125km at 50km/h.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given.
Speed: 50km/h Distance: 125kmSo, to find the time we have to divide the distance by the speed:
We have to apply: time = distance/speed
Replacing with the values given:
Time = 125 / 50 = 2.5 hours
It will take the bus 2.5 hours to travel 125km at 50km/h.
Feel free to ask for more if needed or if you did not understand something.
What is the axis of symmetry of h(x)=5x2+40x+64
Answer:
x = -4.
Step-by-step explanation:
As we have the standard form of a parabola, that is [tex]ax^2+bx+c[/tex] the axis of symetry will be the line [tex]x = \frac{-b}{2a}[/tex]. In this case we have that a = 5, b = 40 and c = 64. Then the axis of symtery is
[tex]x = \frac{-40}{10} = -4[/tex].
.6 is ten times as much as
Answer: 0.6 is ten times as much as 0.06
Step-by-step explanation:
We are given a statement:
0.6 is ten times as much as
Let the number be considered as 'x'
'Times' in the above statement means multiplication operation.
So, the equation for the given statement becomes:
[tex]0.6=10\times x[/tex]
To solve the value of 'x', we shift the number '10' to other side of the equation and operation applied will be division.
Solving the above equation, we get:
[tex]0.6=10\times x\\\\x=\frac{0.6}{10}=0.06[/tex]
Hence, 0.6 is ten times as much as 0.06
how many groups are of sixty are in two hundred forty four
A paddle boat can move at a speed of 14 km/h in still water. The boat is paddled 4 km downstream in a river in the same time it takes to go 2 km upstream. What is the speed of the river?
0645 to 0800is how many minutes
A supermarket had bags of red grapes for $27.09 for 7. They also had bags of green grapes priced at $14.96 for 4. Which type of grapes is most expensive
Convert 4500 feet per second to miles per hour. 5280 ft = 1 mi Round to the nearest hundredth.
Answer: [tex]3068.18\text{ miles per hour}[/tex]
Step-by-step explanation:
We know that 1 hour = 60 minutes
1 minute = 60 seconds
Then by Unitary method , 1 hour=[tex]60\times60=3600\text{ seconds}[/tex]
Also, 5280 ft = 1 mi
Given speed = 4500 feet per second
To convert it into miles per hour. we divide it by 5280 and multiply it by 3600 we get
[tex]4500\times\dfrac{3600}{5280}\\\\=3068.18181818\approx3068.18\text{ miles per hour}[/tex]
Hence, the correct answer = [tex]3068.18\text{ miles per hour}[/tex]
Solve.
−1.5x−3.1<5.5
How are points graphed on a coordinate plane?
(9.32 x 10 3) (3.32 x 10 2)
North America burned 4.5 x 1016 btu of petroleum in 1998. At this rate, how many BTU's will be burned in 9 year?
Follow below steps;
If North America burned 4.5 x 1016 BTU of petroleum in 1998, this rate of consumption can be used to calculate the amount of BTU burned over 9 years. To find the total BTU usage over 9 years, we simply multiply the annual consumption rate by 9.
Annual BTU consumption: 4.5 x 1016 BTU
Consumption over 9 years: 4.5 x 1016 BTU/year * 9 years = 40.5 x 1016 BTU
This calculation shows that North America would have burned a total of 40.5 x 1016 BTU of petroleum over a period of 9 years if the consumption rate remained consistent.
The temperature outside is 0 degrees F. If the temperature drops 14 degrees, what was the overnight low temperature?
The overnight low temperature was -14 degrees F, calculated by subtracting the temperature drop from the initial temperature.
Explanation:In the context of determining the overnight low temperature, it's essential to consider the initial temperature and the subsequent change. In this specific scenario, the starting point is a temperature of 0 degrees Fahrenheit. However, as the night progresses, the temperature experiences a decrease of 14 degrees.
To pinpoint the overnight low temperature, we employ a straightforward subtraction method. By subtracting the amount of change, which is 14 degrees, from the initial temperature of 0 degrees Fahrenheit, we arrive at the final result of -14 degrees Fahrenheit.
This calculation demonstrates the mathematical approach to determining temperature variations, which is especially pertinent in weather forecasting and climatology. It showcases how understanding temperature fluctuations and changes is crucial for assessing climatic conditions and their impact on various aspects of daily life and scientific research.
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Jack is mixing a cleaning solution that is 12% bleach. After mixing the solution, Jack has 150 ounces of cleaning solution. How many ounces of bleach did Jack use.
can someone please help me
Add.
–13 + (–8)
A.
–21
B.
–5
C.
5
D.
21
Two feet is what percent of one yard
Apartment A has a security deposit of $1000 and cost $1200 each month. Apartment B has a $1500 security deposit and cost $1175 each month. How many months will it take for the costs to be the same?
It will take 20 months for the costs of Apartment A and Apartment B to be the same.
Explanation:To find out how many months it will take for the costs of Apartment A and Apartment B to be the same, we need to set up an equation. Let's say it takes x months for the costs to be equal. The equation would be: 1000 + 1200x = 1500 + 1175x. We can solve this equation to find the value of x.
First, we can simplify the equation by subtracting 1175x from both sides: 1000 + 25x = 1500. Then, we can subtract 1000 from both sides to isolate the variable: 25x = 500.
Finally, we can divide both sides of the equation by 25 to solve for x: x = 20. Therefore, it will take 20 months for the costs of Apartment A and Apartment B to be the same.
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choose the compatible numbers that will give the best estimate for 589/58
Answer:
what he said
Step-by-step explanation:
Fencing costs $10.15/ft. A customer purchases 8 3/8 ft of fencing for his yard. How much did the customer pay for the fencing? Round to the nearest cent.