Mathematics : asked on karsynraine8224

14.11.2022

Write a linear function through the points (0,9) and (1,27)

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Step-by-step answer

09.07.2023, solved by verified expert

Mathematics, DAV Post Graduate College

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y = 18x + 9

Explanation:

(0,9), (1,27)

slope:

equation:

y - y₁ = m ( x - x₁)

y - 9 = 18 ( x - 0 )

y = 18x + 9

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Mathematics, DAV Post Graduate College

5 254 answers

Unlock the full answer

y= x + 9

Step-by-step explanation:

(0,9) , (1,27)

(-)÷(-) = slope

=1 =0 =27 =9

(1-0)÷(27-9) = 1/18

m = slope = 1/18

y- = m (x- )

y-9= (x-0)

y-9 = x

y= x + 9

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Helpful Useless

Faq

Mathematics

Write a linear function through the points (0,9) and (1,27)

Step-by-step answer

P Answered by Specialist

y = 18x + 9

Explanation:

(0,9), (1,27)

slope:

$\sf \dfrac{y_2-y_1}{x_2-x_1}$

$\sf \dfrac{27-9}{1-0}$

$\sf 18$

equation:

y - y₁ = m ( x - x₁)

y - 9 = 18 ( x - 0 )

y = 18x + 9

Mathematics

Identify the equation of the linear function through the points (-1,3) and (2, -3). Than state that the rate of change of the function.

Step-by-step answer

P Answered by PhD

1

y = -2x+1

rate of change -2

Step-by-step explanation:

The rate of change of a linear function is the slope

m = (y2-y1)/(x2-x1)

= (-3-3)/(2--1)

= (-3-3)/(2+1)

=-6/3

=-2

We can use point slope form

y-y1 = m(x-x1)

y-3 = -2(x--1)

y-3 = -2(x+1)

Distribute

y-3 = -2x -2

Add 3 to each side

y-3 +3 = -2x-2+3

y = -2x+1

Mathematics

Identify the equation of the linear function through the points (-1,3) and (2, -3). Than state that the rate of change of the function.

Step-by-step answer

P Answered by PhD

1

y = -2x+1

rate of change -2

Step-by-step explanation:

The rate of change of a linear function is the slope

m = (y2-y1)/(x2-x1)

= (-3-3)/(2--1)

= (-3-3)/(2+1)

=-6/3

=-2

We can use point slope form

y-y1 = m(x-x1)

y-3 = -2(x--1)

y-3 = -2(x+1)

Distribute

y-3 = -2x -2

Add 3 to each side

y-3 +3 = -2x-2+3

y = -2x+1

Mathematics

Carlos and Ethan noticed that both proportional relationships and linear functions form a straight line when graphed. Carlos claims that all linear functions are also proportional relationships. Ethan disagreed and tells Carlos that he has it backwards, that all proportional relationships are linear functions. Which statement accurately compares their observations? A) Carlos is correct because all linear functions go through the origin. B) Ethan is correct because all proportional relationships form a straight line and go through the origin and

Step-by-step answer

P Answered by Specialist

3

B. Ethan is correct because all proportional relationships form a straight line and go through the origin and linear functions are linear, but they don’t all go through the origin so they are not always proportional.

Step-by-step explanation:

So a proportional relationship is just a special kind of linear relationship, i.e., all proportional relationships are linear relationships (although not all linear relationships are proportional).

Mathematics

Modeling a Geometric Sequence This activity will help you meet these educational goals: You will model a geometric sequence with an exponential function, graph the function, and make predictions. In 2013, scientists began an annual count of butterflies in Elliot Park. That year, they counted 125 butterflies. In subsequent years, the scientists recorded an increase in the park’s butterfly population at a rate of 20% each year. Based on this information, answer the following questions. Part A Fill in the table with the values for the population of

Step-by-step answer

P Answered by PhD

3

Answers are below, please ask me if something doesn't make sense.

Step-by-step explanation:

so first we set up the equation, in an exponential function it has three parts a*b^x where a is the starting amount, b is 1 + the percent increase (or 1 - the percent decrease) and of course x is every time the increase/ decrease happens.

120*1.2^x

Part A

I don't know the table, but just plug in .

Part B

I guess you weren't supposed to know? or just do the math without having the equation. If you ever have an increase by percents or decimals or fractions repeatedly though its an exponential function. Specifcially if they are multiplied. Linear functionshave a term added or subtracted. Or in other words exponential is a*b^x (so b is being repeatedly multiplied) and linear is mx+b so m is continually added. Do you need help with the checking part?

Part C

Graph the points for 0, 1, 2, 3.

Part D

Geometric because there is a common ratio instead of a common difference (repeated multilying vs repeated adding/ subtracting), which is pretty much the definition of a geometric sequence.

Part E

a recursive function would basically just take the parts of the exponential function. a1 = starting point and a(n) = a(n-1)*the common ratio. To make f(1) = 125 we do have to change the function I gave before. Instead of 125*1.2^x it will be 125*1.2^(x-1) . Part C still has the right numbers since we started with 0.

Part F

I gave you the equation, do you know how you would find it though?

The parameters tell us this only works for 2013 and after

Mathematics

Carlos and Ethan noticed that both proportional relationships and linear functions form a straight line when graphed. Carlos claims that all linear functions are also proportional relationships. Ethan disagreed and tells Carlos that he has it backwards, that all proportional relationships are linear functions. Which statement accurately compares their observations? A) Carlos is correct because all linear functions go through the origin. B) Ethan is correct because all proportional relationships form a straight line and go through the origin and

Step-by-step answer

P Answered by Master

3

B. Ethan is correct because all proportional relationships form a straight line and go through the origin and linear functions are linear, but they don’t all go through the origin so they are not always proportional.

Step-by-step explanation:

So a proportional relationship is just a special kind of linear relationship, i.e., all proportional relationships are linear relationships (although not all linear relationships are proportional).

Mathematics

Part A: A graph passes through the points (0,2), (1,3), and (2,4). Does this graph represent a linear function or a non-linear function? Explain your answer in words. Part B: Write one example of a linear function and one example of a nonlinear function. (Use x and y as the variables)

Step-by-step answer

P Answered by PhD

29

A) linear

B) y = x is linear; y = 1/x is non-linear

Step-by-step explanation:

A) The points lie on the same straight line, so the function is linear.

__

B) Any function that has x to a power other than 1 will be non-linear.

linear function: y = x

nonlinear function: y = x^-1 = 1/x

Mathematics

Modeling a Geometric Sequence This activity will help you meet these educational goals: You will model a geometric sequence with an exponential function, graph the function, and make predictions. In 2013, scientists began an annual count of butterflies in Elliot Park. That year, they counted 125 butterflies. In subsequent years, the scientists recorded an increase in the park’s butterfly population at a rate of 20% each year. Based on this information, answer the following questions. Part A Fill in the table with the values for the population of

Step-by-step answer

P Answered by PhD

3

Answers are below, please ask me if something doesn't make sense.

Step-by-step explanation:

so first we set up the equation, in an exponential function it has three parts a*b^x where a is the starting amount, b is 1 + the percent increase (or 1 - the percent decrease) and of course x is every time the increase/ decrease happens.

120*1.2^x

Part A

I don't know the table, but just plug in .

Part B

I guess you weren't supposed to know? or just do the math without having the equation. If you ever have an increase by percents or decimals or fractions repeatedly though its an exponential function. Specifcially if they are multiplied. Linear functionshave a term added or subtracted. Or in other words exponential is a*b^x (so b is being repeatedly multiplied) and linear is mx+b so m is continually added. Do you need help with the checking part?

Part C

Graph the points for 0, 1, 2, 3.

Part D

Geometric because there is a common ratio instead of a common difference (repeated multilying vs repeated adding/ subtracting), which is pretty much the definition of a geometric sequence.

Part E

a recursive function would basically just take the parts of the exponential function. a1 = starting point and a(n) = a(n-1)*the common ratio. To make f(1) = 125 we do have to change the function I gave before. Instead of 125*1.2^x it will be 125*1.2^(x-1) . Part C still has the right numbers since we started with 0.

Part F

I gave you the equation, do you know how you would find it though?

The parameters tell us this only works for 2013 and after

Mathematics

Part a: a graph passes through the points (0, 2), (2, 6), and (3, 12). does this graph represent a linear function or a non-linear function? explain your answer in words. part b: write one example of a linear function and one example of a non-linear function. (use x and y as the variables) use full sentences and explain fully.

Step-by-step answer

P Answered by PhD

29

Part A

The graph passes through (0,2),(2,6),(3,12) .

If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points.

Using (0,2) and (2,6) .

We obtain the slope to be

$m=\frac{6-2}{2-0}$

$\Rightarrow m=\frac{4}{2}=2$

Using (0,2) and (3,12) .

We obtain the slope to be

$m=\frac{12-2}{3-0}$

$\Rightarrow m=\frac{10}{3}=3\frac{1}{3}$ .

Since the slope is not constant(the same) everywhere, the function is non-linear.

Part B

A linear function is of the form

y=mx+b

where is the slope and is the y-intercept.

An example is y=2x-3

A linear function can also be of the form,

ax+by=c where a,b and are constants.

An example is 2x+4y=3

A non linear function contains at least one of the following,

Product of

and

Trigonometric functionExponential functionsLogarithmic functionsA degree which is not equal to

or

.

An example is xy=1 or y=x^2 or $y=\sqrt{x}$ etc

Mathematics

Part a: a graph passes through the points (0, 2), (1, 3), and (2, 4). does this graph represent a linear function or a non-linear function? explain your answer in words. part b: write one example of a linear function and one example of a non-linear function. (use x and y as the variables)

Step-by-step answer

P Answered by PhD

Part A: Yes, the graph is a linear function. It is a straight line through the graph. No curves, no anything, just a straight line.

Part B: An example of a linear graph is y = x¹. And an example of a non-linear function is y = x².

Explanation:

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