What is the equation of the line represented by the table below?

x y
-3 1
6 4
12 6
30 12

Answers

Answer 1

Answer:

[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]

Step-by-step explanation:

Equation of a Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The table shows the relation between x and y. It contains the following points

(-3,1), (6,4), (12,6), (30,12).

Taking the two first points, we find the equation of the line:

[tex]\displaystyle y-1=\frac{4-1}{6+3}(x+3)[/tex]

[tex]\displaystyle y-1=\frac{3}{9}(x+3)[/tex]

Simplifying:

[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]

To ensure the rest of the points belong to the line, we test them:

For the point (12,6):

[tex]\displaystyle 6-1=\frac{1}{3}(12+3)[/tex]

[tex]\displaystyle 5=\frac{1}{3}(15)[/tex]

5=5

Since equality is true, the point belongs to the line.

For the point (30,12):

[tex]\displaystyle 12-1=\frac{1}{3}(30+3)[/tex]

[tex]\displaystyle 11=\frac{1}{3}(33)[/tex]

11=11

Since equality is true, the point belongs to the line.

Thus, the equation of the line is:

[tex]\mathbf{\displaystyle y-1=\frac{1}{3}(x+3)}[/tex]


Related Questions

Felix can grow 6 plants with every seed packet. Write an equation that shows the relationship between the number of seed packets x and the total number of plants y. Write your answer as an equation with y first, followed by an equals sign.

Answers

Answer:

I believe it’s:

Y= 6x

Step-by-step explanation:

please someone help me please??!!!​

Answers

Answer:

how should I know?

Step-by-step explanation:

Answer:

a.)

x= -2 , -1, 0, 1, 2, 3

y=8 , 7, 6, 5, 4, 3

and for b just plot the point and then connect them. im not sure how i can show you

Step-by-step explanation:

A circular garden has a diameter of 8 feet, and a rectangular garden has side lengths of 5 feet by 9 feet.
find the difference in square feet between the two gardens

Answers

Answer:

rectangular

Step-by-step explanation:

Answer:

The square of a number decreased by 8 times the number equals 9. Determine the two possible values of the number. X2-8x=9. +1-9 ... 9. Basic Area of Rectangles. 16 The length of a rectangular room is 5 less than ... 17 The total area of Jon's backyard is 144 square feet. ... the length of a side of the original square garden.

Step-by-step explanation:

i hope this helps!

Need help in math ASAP

Answers

Answer:

B

Supplementary means they add to make 180 deg, so solve (4x-8)+(2x+2)=180

Answer:

angle a + angle b=180

4x-8+(2x+2)=180

6x-6=180

6x=180+6

x=186/6

{x=31°}

which of the following is an arithmetic sequence with common difference 2
A. 1, -3, 5, -7, 9
B. 2, 4, 8, 16, 32
C. 10, 8, 6, 4, 2
D. 13, 15, 17, 19, 21

Answers

Answer:

C is the answer.

C has a common difference of "2"

Step-by-step explanation:

You could say that the word "difference" also means Subtraction, so in a simpler way of saying "The common difference of 2" you could say, "Which one of the following is subtracting by 2?"

PLEASE MARK BRAINLIEST

I would say C.10,8,6,4,2

What is the total number of servings the modified recipe will make?

Answers

9514 1404 393

Answer:

  B.  4

Step-by-step explanation:

Equating exponents, we have ...

  2x +7 = 15

  2x = 8 . . . . . subtract 7

  x = 4 . . . . . . divide by 2

The equation is true when the value of x is 4.

hope this helps enjoy.

Please Hurry! Due by tonight!

Answers

Step-by-step explanation:

the y-intercept is 1 because it's on the y(axis). the line from 1 goes down 1 over three so the slope is 1/3.

your equation would be y=1/3x+1

Solve each equation. For each step. Identify the property used.

14 + 3n = 8n - 3(n-3)
22x + 11 = 4x - 7

(P.S. The properties that the problem is asking for are the properties of equality. Division property of equality, etc, etc.)

Answers

Answer:

Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2

Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1

Step-by-step explanation:

We will solve the equations one by one

So,

[tex]14 + 3n = 8n - 3(n-3)[/tex]

Applying Distributive property

[tex]14 + 3n = 8n - 3n+9\\14+3n = 5n+9[/tex]

Subtraction property of equality (Subtracting 14 from both sides)

[tex]14+3n-14 = 5n+9-14\\3n = 5n-5[/tex]

Subtraction property of equality (Subtracting 5n from both sides)

[tex]3n-5n = 5n-5-5n\\-2n = -5[/tex]

Division property of equality (Dividing both sides by -2)

[tex]\frac{-2n}{-2} = \frac{-5}{-2}\\n = \frac{5}{2}[/tex]

Second Equation:

[tex]22x + 11 = 4x - 7[/tex]

Subtraction property of equality (Subtracting 11 from both sides)

[tex]22x + 11-11 = 4x - 7-11\\22x = 4x-18[/tex]

Subtraction property of equality (Subtracting 4x from both sides)

[tex]22x-4x = 4x-18-4x\\18x = -18[/tex]

Division property of equality (Dividing both sides by 18)

[tex]\frac{18x}{18} = \frac{-18}{18}\\x = -1[/tex]

Hence

Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2

Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1

Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Irene​'s car had 6.4 gallons in the 14​-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost ​$3.90 per gallon. How much did Irene spend on​ gas?

Answers

Answer:

$24.96

Step-by-step explanation:

Total number of gallons irede had in his tank = 6.4gallons

Price per gallon is $3.90

To get the cost of 6.4gallons;

If 1 gallon = $3.90

6.4gallons = $x

Cross multiply

1 * x = 3.90 * 6.4

x = 24.96

Hence Irene spent $24.96 on gas

Name a ray with an endpoint of A.

Answers

B to A. it passes through E

due soon will give brainalist no fake answers!!

Answers

Answer:

90gr strawberry jelly

6 sponge fingers

315ml custard

135gr tinned fruit

Step-by-step explanation:

120/4 = 30 * 3 = 90

8/4 = 2 * 3 = 6

420/4 = 105 * 3 = 315

180/4 = 45 * 3 = 135

okay so i got (1,1) but it's not on here ;-;

Answers

It’s (0, 4.5).

You can use 0 to substitute for x. That makes (0,4.5) a possible ordered pair. Another possible answer is using 1 or 2, but that is not one of the answers provided. Hope this helped!

The number of avocados ( a ) (a) a particular tree produces each year can be modeled by the function a ( y ) a(y). What does a ( 12 ) = 364 a(12)=364 mean?

Answers

Answer:

[tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.

Step-by-step explanation:

Let [tex]a[/tex] the number of avocados that a particular tree produces at a year. [tex]a(y)[/tex] is the number of avocados that a particular tree produces at y-th year. Hence, [tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.

A 14 foot long ramp is being built to access a front door in a house. The door is 5 feet above the ground. How far away from the base of the house must the ramp be placed? What angle will the ramp make with the ground?

Answers

Answer:

The ramp must be placed 13.08 feet from the base of the house.

The angle the ramp will make with the ground is 20.92°.

Step-by-step explanation:

An illustrative diagram for the scenario is shown below.

In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.

To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.

The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"

In the diagram, the hypotenuse is r

∴ r² = d² + x²

r = 14 ft

d = 5 ft

∴ 14² = 5² + x²

196 = 25 + x²

Then, x² = 196 - 25

x² = 171

x = √171

x = 13.08

Hence, the ramp must be placed 13.08 feet from the base of the house.

Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.

From the formula

Sinθ = Opposite / Hypotenuse

In the diagram, opposite = d = 5ft

and Hypotenuse = r = 14ft

∴ Sinθ = 5ft / 14ft

Sinθ = 0.3571

∴ θ = Sin⁻¹(0.3571)

θ = 20.92°

Hence, the angle the ramp will make with the ground is 20.92°.

For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy???

Answers

Answer: 4 and a half

Step-by-step explanation:

there are 1,920fence posts used in a 12-killometer strech fence how many fence posts are used in one kilometer

Answers

Answer:

160

Step-by-step explanation:

Just divide 1920 into 12

Given: m || n and p is a traversal.
Prove: m<2=m<7
What is the missing reason in the proof?

Answers

Answer:

Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are congruent.

maria wanted to invest $10,000 at the bank. she invested part of her money in a cd account paying 2.1% simple interest and invest the rest of her money in a checking account paying 1.5% simple interest. After 1 year, her interest income was $195. How much did Maria invest in each account

Answers

Answer:I = ?, P = $500, r = 6%, t = 3 years

Step-by-step explanation:

if if x equals 3 and Y equals negative 2 - x 3 - Y2 ​

Answers

Answer:

13

Step-by-step explanation:

x=3, y=-2 so 3(3)-(2)2=13


Jamie tossed a coin 50 times. The coin landed on heads 27 times and landed on tails
23 times. What is the relative frequency of landing on heads?

Answers

Answer: 54%

Step-by-step explanation:

The relative frequency of landing on heads is 0.54 or 54%.

Given that Jamie tossed a coin 50 times.
Head showed for 27 times.

Tails showed for 23 times.

We need to find the relative frequency of landing on heads,

The relative frequency of an event is calculated by dividing the number of times the event occurred by the total number of trials or occurrences.

In this case, Jamie tossed a coin 50 times, and it landed on heads 27 times.

To find the relative frequency of landing on heads, we divide the number of times the coin landed on heads (27) by the total number of tosses (50):

Relative Frequency of landing on heads = Number of heads / Total number of tosses

Relative Frequency of landing on heads = 27 / 50

Simplifying this fraction, we get:

Relative Frequency of landing on heads = 0.54

This means that, based on the given data, the coin landed on heads approximately 54% of the time in the 50 tosses performed by Jamie.

Therefore, the relative frequency of landing on heads is 0.54 or 54%.

Learn more about Relative Frequency click;

https://brainly.com/question/28342015

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Simply.
[tex] \frac{ab - a}{a} = [/tex]
[tex] \frac{2x + y}{y} = [/tex]
I mainly forgot how to do it. Do I divide -ab to get it alone? How do I do it?​

Answers

Answer:

Required Answer:-First go to first equation

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{ab-a}{a}}[/tex]

Take common

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {{\bcancel {a }}(b-1)}{{\bcancel {a}}}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]{\underline{\boxed{\bf b-1)}}}[/tex]

The matrices show the number of indoor and outdoor volunteers in different age groups

create a matrix that shows the total number of indoor and outdoor volunteers in different age groups. name the matrix T.

what is the value of the element t11 and what does the value indicate?

create a matrix by subtracting the women's matrix from the mens matrix. name the matrix D.

what is the value of the element at d12 and what does that value indicate? ​

Answers

Answer:

(a) M + W = Indoor= [26 55] Outdoor = [32 49]

(b) The value indicates the sum of the indoor volunteers ages 18-39 so the Value would be, 34.

(c) M – W = Indoor = [8 15] Outdoor = [-16 3]

(d) This value indicates the difference of the volunteers indoors 40. So the value would be 15.

Step-by-step explanation:

If this is wrong my apologies i tried LOL

but i will let you know when i get the results back asap!

The value of the element t11 is 34 and the value of the element at d12 is 15.

When are two matrices called being equal?

Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.

M + W = Indoor= [26 55] Outdoor = [32 49]

The value indicates the sum of the indoor volunteers ages 18-39,

Therefore, the Value would be, 34.

To create a matrix by subtracting the women's matrix from the mens matrix.

Now the difference;

M – W = Indoor = [8 15] Outdoor = [-16 3]

This value indicates the difference of the volunteers indoors 40 so

Therefore the value would be 15.

Learn more about equal matrices here:

https://brainly.com/question/13430728

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Peter is painting his bedroom. His bedroom has four walls. Yesterday, he painted 1 2/5 walls. What fraction of the walls is left to paint?

Answers

Answer: 2 3/5ths are left or 13/5

Step-by-step explanation: 1 2/5 + 2 3/5 = 4 total walls

Please quickly! Out of 5,500 people who attended the football game, fifty-six percent were rooting for the home team. How many people rooted for the home team?

Answers

3,080 people rooted for the hometeam.

Haley bought 1.6 pounds of almonds for $13.20. How much did she pay per pound for the almonds? Record your answer and fill in the bubbles on your answer document. Be sure to use correct place value. +/- .

Answers

Answer:

She paid $8,25 per pound

Step-by-step explanation:

Given

[tex]Weight = 1.6\ lb[/tex]

[tex]Total= \$13.20[/tex]

Required

Determine the amount paid per pound

To do this, we simply divide the amount by the weight of Almonds.

[tex]Amount = \frac{Total}{Weight}[/tex]

[tex]Amount = \frac{\$13.20}{1.6\ lb}[/tex]

[tex]Amount = {\$8.25/\ lb[/tex]

Hence, she paid $8,25 per pound

The ratio of blueberries to strawberries in a fruit salad is 4:3. If there are 45 strawberries in a salad, how many blueberries are there.. Blueberries 4 Strawberries 3

Answers

Answer:

60 blueberries

Step-by-step explanation:

Given the ratio of blueberries to strawberries in a fruit salad to be 4:3. The total ratio = 4+3 = 7

If there are 45 strawberries in the salad then we can first calculate the total mixture of both as shown;

amount of strawberries = 3/7 * x = 45

x is the total amount of mixture

from the expression;

3x/7 = 45

cross multiply

3x = 7*45

3x = 315

x = 315/3

x = 105

The amount of blueberries present = 105 - 45 = 60

Hence the amount of blueberries present is 60 blueberries

how do I do this?
I don't understand geometry and it's really confusing can one of you help me? ​

Answers

Answer:

lol im stuck too

Step-by-step explanation:

Solve the following equation:
a/3.5 - 4.8 = 6.3
a= ______

Answers

Answer:

a= 38.85

Step-by-step explanation:

Answer:

[tex]\boxed {a = 38.85}[/tex]

Step-by-step explanation:

Solve for the value of [tex]a[/tex]:

[tex]\frac{a}{3.5} - 4.8 = 6.3[/tex]

-Add both sides by [tex]4.8[/tex]:

[tex]\frac{a}{3.5} - 4.8 + 4.8 = 6.3 + 4.8[/tex]

[tex]\frac{a}{3.5} = 11.1[/tex]

-Multiply both sides by [tex]3.5[/tex]:

[tex]a = 11.1 \times 3.5[/tex]

[tex]\boxed {a = 38.85}[/tex]

Therefore, the value of [tex]a[/tex] is [tex]38.85[/tex].

Solve for the variable
-3/4b = 2

Answers

Answer:

b = 2.666.......

Step-by-step explanation:

[tex]-\frac{3}{4} b = 2[/tex]

------    -----

[tex]-\frac{3}{4}[/tex]      [tex]-\frac{3}{4}[/tex]

b = 2.666.....

Use the quadratic formula to solve the equation.
5x2-3x + 1 = 0
X=

Answers

Answer:

x= 11/3

Step-by-step explanation:

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