Why is y=mx+b the slope intercept form
Answers
Answer:
In the equation of a straight line (when the equation is written as "y = MX + b"), the slope is the number "m" that is multiplied by the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).
Answer: The equation defines the relationship between the angle of inclination of the line relative to the x-axis and the point at which the line passes through the y-axis on a graph.
Step-by-step explanation:
Imagine a line, L, that passes through the y-axis of a graph at some point B=(0,b), where the 0 is the x-coordinate of B and b is the y-coordinate of B. In this case, we will use the variable m to represent the slope of the line. Geometrically, the slope of a line is said to be tangent to its angle of inclination, the smaller of the two angles formed by the line L and the x-axis. In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the side opposite of it over the side adjacent to it. This relationship can be illustrated by constructing a right triangle where the hypotenuse is formed by the segment of the line L between the point B and an arbitrary point P somewhere along the line with the coordinates (x,y).
This triangle can be seen in the attached jpg. The side opposite of the angle of inclination is the imaginary vertical line formed between the point P and the x axis and the side adjacent to it is formed by the imaginary horizontal line between the point B and the vertical line from P. The point where these imaginary lines intersect forms the right angle of the triangle. The length of the opposite side, l1, can be expressed as the difference in y between points P and B:
l1 = y-b
Likewise, the length of the adjacent side, l2, can be expressed as the difference in x between points P and B:
l2 = x-0
The tangent of the angle of inclination, labled as [tex]\alpha[/tex] in the picture, can then be expressed as:
tan([tex]\alpha[/tex]) = [tex]\frac{(y-b)}{(x-0)}[/tex]
simplified as:
tan([tex]\alpha[/tex]) = [tex]\frac{y-b}{x}[/tex]
Because we know that slope m = tan([tex]\alpha[/tex]), we can say that
m = [tex]\frac{y-b}{x}[/tex]
solving by algebra for y,
mx + b = y or y = mx + b
in single variable calculus, the slope of a line is described as the rate of change of its y coordinates with respect to the rate of change of its x coordinates, referred to as the derivative of y with respect to x. This relationship is used to describe things like the speed of an object as it relates to the change in the objects position. The important thing to realize here is the connection between the slope, which we expressed as the difference in the y values of two points on a line over the difference in their x values, and the behavior of the coordinates of points as you move along the line.
Hope that helps! If the last bit is confusing, don't worry, as long as you understand why y=mx+b is the slope intercept form you've got the right idea.
Related Questions
f(x) = x
f(x) = 3
f(x) = 5-x
f(x) = 3-x
Domain
x=2
2
0≤x<2
3
f(x) = 1
f(x) = 2
Function Equation
Answers
Given f(x)=2−∣x−5∣
Domain of f(x) is defined for all real values of x.
Since, ∣x−5∣≥0⟹−∣x−5∣≤0
⟹2−∣x−5∣≤2⟹f(x)≤2
Hence, range of f(x) is (−∞,2].
suppose that among the 6000 students at a high school, 1500 are taking honors courses and 1800 prefer watching basketball to watching football. if taking honors courses and preferring basketball are independent, how many students are taking both honors courses and prefer basketball to football?
Answers
Students taking both honors courses and prefer basketball to football is 450.
Total number of students at a high school = 6000
Number of students who has taken honors courses = 1500
Number of students who prefer watching basketball to football = 1800
Let event of taking honors courses be A
and event of preferring watching basketball be B
P(A) = 1500 / 6000 = 0.25
P(B) = 1800 / 6000 = 0.3
If both the event of taking honors courses and preferring watching basketball is independent then
By using property of independent events ,
P(A∩B) = P(A) . P(B)
= (0.25)(0.3) = 0.075
Number of students taking both honors courses and prefer basketball to football = 0.075 × 6000
= 450 Students
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Write ap text-style pseudocode for a linear search that searches through a list to find an item x. It should display found if the x is equal to an item in the list.
Answers
list <- value, value, value, value
x<-value
FOR EACH item IN the list
{
IF item=x
display "found"
}
Pseudocode is an informal manner of programming description that does not require any strict programming language syntax or underlying era concerns. it is used for growing an outline or a rough draft of a program. Pseudocode summarizes an application's flow but excludes underlying info.
Pseudocode is a synthetic and casual language that facilitates programmers' to increase algorithms. Pseudocode is a "text-primarily based totally" element (algorithmic) layout device. The policies of Pseudocode are fairly straightforward. All statements showing "dependency" are to be indented. the Python pseudocode is a syntax-loose representation of code. So, the Python pseudocode no longer involves any code in it. The Python pseudocode should be a very near illustration of algorithmic good judgment.
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According to a study conducted by an organization, the proportion of americans who were afraid to fly in 2006 was 0. 10. A random sample of americans results in indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of americans who are afraid to fly has.
Answers
According to the the concept of hypothesis testing, there is no evidence that the proportion of Americans who are afraid to fly has decreased.
Hypothesis testing:
Basically, in math hypothesis, it test the population on the basis of the sample data taken from the population using a simple random sampling.
Given,
According to a study conducted by an organization, the proportion of Americans who were afraid to fly in 2006 was 0. 10. A random sample of 1300 Americans results in 117 indicating that they are afraid to fly.
Now, we need to explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has.
While we looking into the given question,
Sample size, n = 1300
Number of Americans who were afraid to fly, x = 117
Now, we have to computing the sample proportion of Americans who afraid to fly,
Therefore, p = 117 / 1300 = 0.09
Then the Formulation of Hypotheses is written as,
Here the Null Hypothesis: H0: p≥0.10
And the alternative Hypothesis: Ha: p<0.10
Then the Left-tailed test of Test statistic is written as,
Here Let us assume that the level of significance, α = 0.05.
Then the Critical value, z≈−1.645
And the Decision rule is written as
If the value of |z|<|z0.05|≈1.645: Do not reject the null hypothesis.
Otherwise If value of |z|≥|z0.05|≈1.645: Reject the null hypothesis.
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What is the range of the given function?
Responses
y≤3y is less than or equal to 3 - no response given
y≤0y is less than or equal to 0 - no response given
−6≤y≤3−6≤y≤3 - no response given
R (all real numbers)
Answers
The range of the given function, using it's concept, is given by the following option.
y≤3: y is less than or equal to 3.
How to obtain the range of a function?The range of a function is the set that is composed by all the output values on a function.
Om the graph of a function, we have that:
The input values are given by the x-axis, that is, by the horizontal axis.The output values are given by the y-axis, that is, by the vertical axis.Hence from the graph, the range of the function is given by the values of y of the function.
From the graph of the function given at the end of the answer, the function assumes values of 3 and greater, hence the first option is the correct option giving the range of the function.
Missing InformationThe function is given by the image presented at the end of the answer.
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Distribute and then Combine Like Terms: 5(3x + 4) + 7x
Answers
Answer:
22x + 20
Step-by-step explanation:
Distribute:= (5)(3x) + (5)(4) + 7x
= 15x + 20 + 7x
Combine Like Terms:= 15x + 20 + 7x
= (15x + 7x) + (20)
= 22x + 20
Answer:
22x +20
Step-by-step explanation:
5(3x + 4) + 7x
5 x 3x + 5 x 4 +7x
15x + 5 x 4 + 7x
15x + 20 + 7x
22x + 20
Find the distance between the points ( – 9.3,3) and ( – 9.3, – 7.5).
Answers
We have that the data is: (x₁ =–9.3, y₁=3) and (x₂=– 9.3, y₂=–7.5). The formula to calculate two distance between two points is:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(x_1-x_2)^2+(y_1-Y_2)^2 } } \end{gathered}$}}[/tex]
When we calculate the distance between two points, we solve what goes inside the parentheses, then it is calculated to the power of 2, and we continue adding the two numbers of the previous results, and finally the square root is calculated.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(-9.3-(-9.3))^2+(-7.5-3)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(0)^2+(-10.5)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{0+110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=10.5 } \end{gathered}$}}}[/tex]
The distance between the points ( – 9.3,3) and ( – 9.3, – 7.5) is 10.5(1 point) college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. how many randomly selected student
Answers
Probability Theory
P (K) =[tex]\frac{n (K) }{n (S)}[/tex]
P(K) : probability of selected K
n (K) : number of occurence of K
n (S) : number of all occurence
In question is not contain information about the number of students who curry a gun, knife, or other weapon and the number of all students. so, we can desribe that :
n (A) : the number of occurence of students who curry a gun
n (B) : the number of occurence of students who curry a knife
n (C) : the number of occurence of students who curry other weapon
and the number of all students is n ( A U B U C) -> union of sets
how many randomly selected student? in question, there is no specific about the student. so, we can answer with :
1) probability of students who curry a gun
P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex]
2) probability of students who curry a knife
P (B) = [tex]\frac{n (B) }{n (AUBUC)}[/tex]
3) probability of students who curry other weapon
P (C) = [tex]\frac{n (C) }{n (AUBUC)}[/tex]
and if question want to estimate with percentage, we can multiply with 100%. example :
1) percentage of probability of students who curry a gun
P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex] x 100%
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Tony planned to spend $100 for food this week. On Monday he spent $22 and on Thursday he spent $52. How much money dose he have left for the week
Answers
Answer:$26
Step-by-step explanation:
52+22=74
100-74=26
What is a, the starting term, for the function: f(x) = 300(1.16)^x?
Answers
The starting term of the function f(x) = 300 (1.16)^x is 300
What is an exponential function?This is a type of function that are of 3 main parts
the starting or initial valuebase function the exponentsConsidering the given problem, f(x) = 300(1.16)^x
the starting = 300
the base = 1.16
the exponents = x
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.
The base is what determines exponential growth or decay
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3. What equation matches the graph below?
Answers
Answer:
B, or y - 1 = 1/2(x + 2)
Step-by-step explanation:
when you solve B, you get y = 1/2x + 2, which is the equation being shown on the graph.
a research team believes that a recently discovered treatment will have an effect on the dependent variable. they randomly selects a sample of 12 people, and with their permission, provides them a treatment. they then evaluate the evidence regarding whether their treatment had an effect. here's the data: the mean for their sample is 99. the mean for the population is 102, with a standard deviation of 11. assume a normal distribution for the individual scores. the research team sets their alpha level to .05. . calculate the z test, and decide whether the research team should: 0 - retain the null hypothesis 1 - reject the null hypothesis.
Answers
Using the z test the value of z is -0.9404 and the value of z the research team should 0 - retain the null hypothesis.
In the given question,
They randomly selects a sample of 12 people, and with their permission, provides them a treatment.
So n = 12
The mean for their sample is 99.
x = 99
The mean for the population is 102.
μ=102
A standard deviation of 11.
σ = 11
Test statistic z:
z = (x-μ)/σ /√n
Now putting the value
z = 99-102/11/√12
z=-3/11/3.45
z=-3/3.19
z= -0.9404
Test statistic z = -0.9404
From the value of z the research team should 0 - retain the null hypothesis.
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A dog kennel charges $40 for each night the dog stays in the kennel. Each day includes a 2 hour play time and
1 hour etiquette training. The kennel also charges a $10 bathing fee for a bath before the dog returns home.
Think of the linear function that demonstrates the cost of putting a dog in the kennel (c) in terms of the number
of nights (n)
Answers
Answer:
c=40n+10
Step-by-step explanation:
They charge 40$ per night from which we get 40n
The extra 10$ is from the bathing fee
The rest of the information they give us isn't useful in this case because they didn't ask us the cost per hour
Determine the measure of each missing angle:
Angle f= 69
Angle g= 69
Angle h= ??
I found G and F but I’m stuck on H please help me!!
Answers
Answer:
Angle f = 69°Angle g = 69°Angle h = 125°Step-by-step explanation:
Angles f and g are congruent as opposite sides are congruent. Therefore:
g = f = (180° - 42°)/2 = 138°/2 = 69°Angles h, 76°, g and the right angle all together form 360°:
h + 76 + g + 90 = 360h + 166 + 69 = 360h + 235 = 360h = 360 - 235h = 125a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) how fast is the radius of the balloon changing at the instant the radius is 50 centimeters?
Answers
0.015 the radius of the balloon changing at the instant the radius is 50cm
given that
a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute
radius = 50 centimeters
now we need to find the volume of the balloon
Let V = volume of the balloon at time t
r = radius of the balloon at time t
V = (4/3)πr3
Given: dV/dt = 500
Find: dr/dt when r = 50
dV/dt = (4/3)(3πr^2)(dr/dt)
500 = 4π(50)^2(dr/dt)
dr/dt = 1/(20π)
dr/dt = 0.015 cm/min
0.015 the radius of the balloon changing at the instant the radius is 50cm
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I need help with this, I "apparently get it wrong"
Answers
Answer:
Step-by-step explanation:
Which one adds up to 14 is the question? There are dots on the dice which correspond to numbers. The dots are saying that they are numbers. And if you get to 14 with the dices, you pick it.
v/7 + 7.1 = -4.1 solve for v
Answers
V/7=-11.2
Multiply the answer by 7
V=-78.4
Answer:
v = -78.4
Explanation:
To solve this, we’re going to need “v” left on one side on its own.
To do this, first get rid of +7.1 by taking it away from both sides of the equation. This leaves v/7 = -11.2
Then multiply by 7 on both sides to get rid of the “divide by 7”. This leaves “v = -11.2 multiplied by 7”.
Multiplying this out gives v = -78.4.
In the space provided below, solve the equation 4x² 768 = 0 for x algebraically. Write your answer in simplest radical form. Show all work.
Answers
Answer:
Step-by-step explanation:-b± √b²-4ac. X =
The length of a rectangle is four more than triple the width. If the perimeter is 160 inches, find the dimensions.
Answers
The length and the width of the rectangle are 61 inches and 19 inches, respectively
How to determine the dimensions of the rectangle?The mathematical statement from the question is given as
Length of a rectangle is four more than triple its width.
Mathematically, this can be represented as
Length = 3Width + 4
The perimeter is given as
Perimeter = 160 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (3Width + 4 + Width) = 160
Divide by 2
3Width + 4 + Width = 80
This gives
4Width= 76
Divide by 4
Width = 19
Recall that
Length = 3Width + 4
So, we have
Length = 3 * 19 + 4
Evaluate
Length = 61
Hence, the dimensions are 61 inches by 19 inches
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QUESTION 8/10 HELP ASAPP
Answers
Answer:
y = - 2x - 4=================
The slope- intercept form:
y = mx + bUse two points on the graph to find the slope:
(-2, 0) and (0, - 4)Find the slope:
m = (- 4 - 0)/(0 - (-2)) = - 4/2 = - 2The y-intercept is b = - 4.
The equation is:
y = -2x - 4What constant would be added to the expression x^2+8/3x in order to make it a perfect square
Answers
Answer:
Hence, the value of y = b^2 = (-3/2)^2 = 9/4 is your answer
Step-by-step explanation:
only if your answers are
A) 3/2
B) 9/4
C) 6
D) 9
Radius: 6 mm
Diameter: 12 mm
Area:
Answers
Answer:
The area of the circle would be 113.04
Step-by-step explanation:
If you plug the radius into the formula for finding the area of a circle (π·r²), or (3.14 · r²) then you'll get 113.04
Hope this helps! :D
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Mr. Fitch needs to get a loan to replace the air-conditioning system in his home.
The cost of the replacement, including installation, is $4,348.00.
He can apply for a 5-year loan or a 3-year loan.
Both loans involve simple interest with an annual interest rate of 6.5%.
If Mr. Fitch applies for the 5-year loan, how much more will he pay in interest than with the 3-year loan?
Answers
If Mr. Fitch applies for the 5-year loan, the amount he will pay in interest with the 3-year loan is: $565.24.
How to find the interest amount?First step is to find the cost of replacement left
Cost of replacement = $4,348 x 6.5%
Cost of replacement =$282.62
Second step is to calculate the amount of 5-year loan
Loan = $282.62 x 5
Loan = $1413.1
Third step is to calculate the amount of the 3-years loan
Loan = $282.62 x 3
Loan = $847.86
Now let find the amount he will pay in interest with the 3-year loan
Amount = $1,413.1- $847.86
Amount =$565.24
Therefore the interest amount is $565.24.
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List the first 5 multiples
4:
3:
9:
12:
Answers
Answer:
Step-by-step explanation:
3 * 4 = 12 3 * 5 = 15 List of the First 5 Multiples of 3: 3, 6, 9, 12, 15 Notes: The listed multiples are the First 5 Multiples of 3 that are positive (greater than 0) The sum of the digits in Multiples of 3 are divisible by 3
Sketch and Solve. A rectangular page is 2 inches longer than it is wide. If the diagonal of the pag is 52 inches, what is the perimeter of the page
Answers
The Perimeter of the Rectangle is 144cm;
What is the Perimeter of a Rectangle?
The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.
The lengths of a rectangle's diagonals are equal. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.
According to the question
Let the length of the rectangle be x cm;
So, The breadth of the rectangle will be: (x+2) cm;
And, we have the diagonal = 52 cm;
So,
we can use the Pythagoras triangle to find the value of x cm;
⇒[tex]x^{2} + (x+2)^{2} = (52)^{2}[/tex]
⇒[tex]2x^{2} +4+4x = 2704;\\[/tex]
⇒[tex]2x^{2} +4x = 2700[/tex]
⇒[tex]2x^{2} +4x - 2700 =0;[/tex]
By solving the above equation, we get:
x = 35 cm;
So, the length of the rectangle = is 35 cm;
Breadth of the rectangle = 37 cm;
and
Perimeter of the Rectangle = 2(35 + 37) cm;
The perimeter of the Rectangle = = 144 cm;
Hence,
The perimeter of the Rectangle = = 144 cm;
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True or false: The numerical coefficient of 14xy4z5 is 4.
Answers
Answer:
False
Step-by-step explanation:
The numerical coefficient is 14, not 4.
Answer:
it's False
Step-by-step explanation:
Trust me IT worth it
Suppose you are able to download 1 free song to your tablet daily and each additional download costs $0. 59. If your monthly bill is $15. 34, how many songs did you download if you downloaded 28 free songs? write an equation and solve for the unknown variable.
Answers
For the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including 28 free songs is equal to 54 songs.
As given in the question,
Total free download songs is equal to 28
Let us consider variable 'x' to represent the number of downloaded songs at the rate of $0.59
Total monthly bill of downloaded songs = $15.34
Equation formed :
0.59x = $15.34
⇒ x = 15.34 / 0.59
⇒ x = 26 songs
Total number of downloaded songs including 28 free songs
= 26 + 28
= 54 songs
Therefore, for the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including 28 free songs is equal to 54 songs.
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What is the value of 43?
Responses
Answers
Please make sure to give me a heart it helps. Thank you.
The Answer is : 64
I took the test and it showed this is the correct answer, hope this helped :)
a number increased by 6 is 30
Answers
Answer:
the number is 24 good luck :)
Answer:
24
Step-by-step explanation:
1) Break down the question
We are told that a number increased by 6 is 30 meaning a number added to 6 will get 30.
2) Work you way backwards to get your answer
To find the answer to this question we have to subtract 30 from 6.
This is because we are told that a number is added to get 30 so we should subtract to find our number!
30 - 6 = 243) Check you answer
Every question that you may be unsure of or had been struggling with should always be checked.
To check our answer we have to go backwards and see if the numbers match
24 + 6 = 30As we can see the numbers match together and are correct in our equation
Hope this helps, have a great day!
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
11r+2
Step-by-step explanation:
combine the two numbers with the same variable and then leave the 2 by itself, that would be 4r+7r=11r and then bring the 2 down that makes 11r+2