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
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y = 18x + 9

Explanation:

(0,9), (1,27)

slope:

Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35

Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35

Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35

equation:

y - y₁ = m ( x - x₁)

y - 9 = 18 ( x - 0 )

y = 18x + 9

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y= Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35x + 9

Step-by-step explanation:

(0,9) , (1,27)

(Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35-Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35)÷(Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35-Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35) = slope

Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35=1    Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35=0    Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35=27    Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35=9

(1-0)÷(27-9) = 1/18

m = slope = 1/18

y- Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35 = m (x- Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35)

y-9= Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35 (x-0)

y-9 = Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35x

y= Write a linear function through the points (0,9), №18010133, 14.11.2022 07:35x + 9

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Faq

Mathematics
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
Step-by-step answer
P Answered by PhD

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
Step-by-step answer
P Answered by PhD

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
Step-by-step answer
P Answered by Specialist

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
Step-by-step answer
P Answered by PhD

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
Step-by-step answer
P Answered by Master

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
Step-by-step answer
P Answered by PhD

  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
Step-by-step answer
P Answered by PhD

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
Step-by-step answer
P Answered by PhD

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 m is the slope and b 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 c are constants.

An example is 2x+4y=3


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

Product of x and yTrigonometric functionExponential functionsLogarithmic functionsA degree which is not equal to 1 or 0.

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

Mathematics
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:

I just did this on FLVS on 12/17/2021!

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