Find the equation of the line, in slope-intercept form, that passes through the points (-2, -4) and (2,8).A) y = 1/3x + 22/3B) y = 3x + 14C) y = 3x + 2 D) y = - 3x + 14

Answers

Answer 1

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

The formula for calculating slope is expressed as

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

where

x1 and y1 are the x and y coordinates of the initial point

x2 and y2 are the x and y coordinates of the final point

From the information given, the initial point is (- 2, - 4) and final point is (2, 8)

Thus,

x1 = - 2, y1 = - 4

x2 = 2, y2 = 8

By substituting these values into the slope formula,

m = (8 - - 4)/(2 - - 2) = (8 + 4)/(2 + 2) = 12/4 = 3

We would find the y intercept, c by substituting m = 3, x = - 2 and y = - 4 into the slope intercept equation. We have

- 4 = 3 * - 2 + c

- 4 = - 6 + c

Adding 6 to both sides of the equation,

- 4 + 6 = - 6 + 6 + c

c = 2

By substituting m = 3 and c = 2 into the slope intercept equation, the equation of the line is

C) y = 3x + 2


Related Questions

Rachel says when she ran 115 yards she went farther than beth who only ran 327 feet. Is Rachel correct?

Answers

Rachel is correct because Rachel ran farther than Beth .

In the question ,

it is given that ,

Rachel ran 115 yards and Beth ran 327 yards ,

For comparing both the distance , we need to convert both the distance in the same unit ,

So , we convert yards to feet ,

we know that,

1 yard = 3 foot  ,

So, 115 yard = 3*115 = 345 feet ,

Rachel ran 345 feet and Beth ran 327 feet .

hence , we can conclude that Rachel ran 345 feet which is greater than Beth , who ran only 327 feet .

Therefore , Rachel is correct because Rachel ran farther than Beth .

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help meeeeeeeeeeee pleaseee

Answers

The solution of the composite function is as follows:

(f + g)(x) = 9x + 1(f - g)(x) = -7x - 17 (f. g)(x) = 8x² - 55x - 72(f / g)(x) =  x - 8 / 8x + 9

How to solve composite function?

Composite functions are when the output of one function is used as the input of another.

In other words, a composite function is generally a function that is written inside another function.

Therefore,  the composite function can be solved as follows:

Therefore,

f(x) = x - 8

g(x) = 8x + 9

Hence,

(f + g)(x) = f(x) + g(x)  = x - 8 + 8x + 9 = 9x + 1

(f - g)(x) = f(x) - g(x)  = x - 8 - ( 8x + 9 ) = x - 8 - 8x - 9 = -7x - 17

(f. g)(x) = f(x) . g(x) = (x - 8)(8x + 9) = 8x² + 9x - 64x - 72 = 8x² - 55x - 72

(f / g)(x) = f(x) / g(x) = x - 8 / 8x + 9

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4x-6a(8x)/98y Solve for x

Answers

1) Solving for x, the following equation:

We're going to isolate the x variable on the left:

[tex]4x-6a\frac{8x}{98y}[/tex]

The line plot below shows the number of minutes dog owners in a certain neighborhood spent walking their dogs last month.Which statement describes the data shown?The data has a range of 150 to 40, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 20, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.The data has a range of 150 to 20, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 40, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.

Answers

Looking at the graph, the minimum value is 40 and the maximum value is 150, therefore the range is between 150 and 40.

Also, we have a total of 27 points on the graph, which means the median is the 14th value of the data set in crescent order.

Counting the points from the left to the right, the 14th point has a value of 100, therefore the median is equal to 100.

So the correct option is

4 students from a class of 15 are going to be chosen to be on the dance committee. Findthe number of different 4-person committees that can be made.

Answers

Answer:

[tex]C(15,4)=1365\text{ different committees}[/tex]

Step-by-step explanation:

This situation can be approached using the formula for combinations:

[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ \text{where,} \\ n=\text{ number of possible items that can be }selected \\ r=\text{ number of items that were selected} \end{gathered}[/tex]

Therefore, solve for n=15 and r=4.

[tex]\begin{gathered} C(15,4)=\frac{15!}{4!(15-4)!} \\ C(15,4)=1365\text{ different committees} \end{gathered}[/tex]

1) An elevator starts at the ground floor, where the ground floor is considered floor 0.It travels up 8 floors before going down halfway to the ground. Next, it travels back up 12 more floors before going down 13 floors. What floor is the elevator on now?

Answers

Answer:

3

Step-by-step explanation:

So, your starting at zero then up eight, and down halfway so four, then back up twelve so its at sixteen, then down thirteen so your answer is three.

Solve this system of equations by graphing. First graph the equations, and then type the solution.y=–4/3x–5x=–3

Answers

we have the system

y=–4/3x–5 ------> equation A

x=–3 ------> equation B

Using a graphing tool

see the attached figure

the solution of the system of equations is the intersection point both lines

the solution is the point (-3,-1)

Malachi is making a fruit smoothie. In addition to a frozen banana, he wants to add one other fruit and one small container of yogurt.

If he has four different options for fruit (blueberries, strawberries, peaches, and raspberries) and three different options for yogurt flavors (plain, vanilla, and lemon), how many fruit smoothie combinations are possible?

There are
possible fruit smoothie combinations.

Answers

Answer:

12 different combinations are possible (I think)

Step-by-step explanation:

Let's try to understand,

1. Blueberries + Plain Yogurt

2. Strawberries + Plain Yogurt

3. Peaches+ Plain Yogurt

4. Raspberries + Plain Yogurt

5. Blueberries + Vanilla Yogurt

6. Strawberries +VanillaYogurt

7. Peaches+ VanillaYogurt

8. Raspberries + VanillaYogurt

9. Blueberries + Lemon Yogurt

10. Strawberries + Lemon Yogurt

11. Peaches+ Lemon Yogurt

12. Raspberries + LemonYogurt

I hope this is the right answer and if not please forgive.

2 is less than or equal to y

Answers

Solution

[tex]2\leq y[/tex]

See attached pic for problem. Only need help with part D

Answers

For the given question, we will use the formula from part (b) to answer part (d)

The given function is as follows:

[tex]S=260.4914\cdot A^{0.2051}[/tex]

We will find the number of species (S) When A = 813

so, substitute with A = 813, then find S

[tex]S=260.4914\cdot813^{0.2051}\approx1029.563[/tex]

Rounding the answer to the nearest 10 species

So, the answer will be:

[tex]S=1030[/tex]

Price of PensWhat is the slope ofthe line?Price ($)0-NW A o ovo2Give your answer asa fraction in simplestform.11 2 3 4 5 6 7 8 9Number of Pens

Answers

Solution

For this case we can select the following two points:

(0,0) and (4,6)

We can find the slope using this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-0}{4-0}=\frac{3}{2}[/tex]

then the answer after simplify would be:

3/2

Lisa is four years younger than her sister. Which expression below stands for the sum of Lisa’s age and her sister’s age?
A. x − (x − 4)
B. (x + 4) − x
C. None of these
D. (x − 4) − x

Answers

The expression for the sum of Lisa and her sister's age is (x - 4) + x  which is the third option that is none of these form the given options.

It is given in the question that Lisa is four years younger than her sister.

Let Lisa's sister's age be x years.

Hence, according to the data given on the question, we can write,

Lisa age = (x - 4) years

Hence, the expression for the sum of the ages of Lisa and her sister will be = (x - 4) + x years.

It is not given in any of the options, hence the answer is none of these.

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You have an investment account that has a balance of $50,000. If the account iscompounded daily and has an interest rate of 4%, how much did you originally depositinto the account 10 years ago?

Answers

Since we know the future alue of the account, using the formula for the compounded interest with n = 365 (since the account is compounded daily), t=10, r = 4% and A=50000 in the following equation:

[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex]

using these values and solving for P, we get:

[tex]\begin{gathered} 50000=P(1+\frac{0.04}{365})^{365\cdot10} \\ \Rightarrow P=\frac{50000}{(1+\frac{0.04}{365})^{3650}}=33516.74 \\ P=33,516.74 \end{gathered}[/tex]

therefore, the original amount deposited 10 years ago is $33,516.74

A red die is tossed and then a green dieis tossed. What is the probability thatthe red die shows a six or the green dieshows a six?Hint: The two events are not mutually exclusive. So to the find theprobability of the union, use:P(A or B) = P(A) + P(B) - P(A and B)[?]

Answers

Let's call the event of the red die to show a six as event A, and the event of the green die to show a six as event B.

The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. On both dices, we have 6 possible outcomes(the numbers from 1 to 6), with one favourable outcome(the number 6), therefore, the probabilities of those events are:

[tex]P(A)=P(B)=\frac{1}{6}[/tex]

Each roll is independent from each other, then, the probability of both events happening simultaneously is given by their product:

[tex]P(A\:and\:B)=P(A)P(B)[/tex]

Using the additive rule of probability, we have the following equation for our problem:

[tex]\begin{gathered} P(A\:or\:B)=P(A)+P(B)-P(A\:and\:B) \\ =P(A)+P(B)-P(A)P(B) \\ =\frac{1}{6}+\frac{1}{6}-\frac{1}{6^2} \\ =\frac{2}{6}-\frac{1}{36} \\ =\frac{12}{36}-\frac{1}{36} \\ =\frac{12-1}{36} \\ =\frac{11}{36} \end{gathered}[/tex]

the probability that the red die shows a six or the green die shows a six is 11/36.

Which of the following numbers is divisible by 6?
A. 342 543
B. 322 222
C. 415 642
D. 123 456​

Answers

To be divisible by 6 it must be even and have a digit sum divisible by 3
A. 342 543 is odd
B. 322 222 is even but the digits add to 13 which is not a multiple of 3
C. 415 642 is even but the digits add to 22 which is not a multiple of 3
D. 123 456 is even and the digits add to 21 so it is a multiple of 6
123 456 / 6 = 20 576 with no remainder

What is the value of x? Enter your answer in the box. x =

Answers

Step-by-step explanation:

it is an equilateral triangle : all 3 sides are if equal length (indicated by the same symbol on each side).

automatically with that comes the conclusion that all 3 angles have the same size.

and since the sum of all angles in a triangle is always 180°, this means every angle is 180/3 = 60°.

therefore,

2x - 4 = 60

2x = 64

x = 32

and FYI

5y = 60

y = 12

Which graph IS a function?

Answers

A is a function. It sounds hit the same point on the X-axis more than once.

Answer:

Graph A

Step-by-step explanation:

It is a function of f(x) = 2

Which of the following IS a function?

Answers

C because you just have to find which one doesn’t have a repeating X value. All of the other answers repeated an x value at least once so C is the right answer

Answer:

The ans C hope it helps u

have a good day

What is the area of this triangule? h = 12 in, b = 3 in

Answers

Answer:

Area = 18

Explanation:

The area of a triangle is given by

Area = 1/2 height * base length

Now in our case

height = 12 in, base length = 3 in; therefore, the area is

Area = 1/2 * 12 * 3

Area = 6 * 3

Area = 18

Which is our answer!

Can you help me find the answer to this equation

Answers

Given:

K is the mid-point of FG and L is the mid-point FH.

To find:

The measure of Angle H

Step-by-step solution:

As we are given that K and L are the midpoints of FG and FH respectively.

According to the mid-point theoram,

The segment that connects the mid-point of two sides, is parallel to the third side of that triangle.

Thus,

KL||GH and ∠KLF = ∠GHL

As both of these angles are corresponding angles.

So we can say that m∠H = 85 degrees.

A total of 350 pounds of cheese is packaged into boxes each containing 1 5 pointsand 3/4 pounds of cheese. Each box is then sold for $1.75. What is the totalselling price of all of the boxes of cheese?150350450550

Answers

To solve the exercise, you can first know how many boxes of cheese result with the amount of 350 pounds of cheese.

For this, you can use the rule of three, like this

[tex]\begin{gathered} 1\text{ box}\rightarrow1\frac{3}{4}\text{ pounds of cheese} \\ x\text{ boxes}\rightarrow350\text{ pounds } \end{gathered}[/tex]

So, you have

[tex]undefined[/tex]

A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2,3,4. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 1 is an example of which of the following events? Select all correct answers.

Answers

The event Red 1 is an example of these following events:

R and O.E'.E or R.

Which events are included into Red 1?

Red cards are represented by the letter R, while the number 1, which is odd, is represented by the letter O.

Both events R and O happen in the, hence the event R and O is one of the possible events to this problem, as the card is both red and has an odd number.

The number is not even, hence the event E' is another one of the events in this problem.

The final event is E or R, as the card has a red number, meaning that at least one of the options E or R are satisfied.

Missing information

The options which the event respect are missing, and are given by the image at the end of the answer.

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The perimeter of a rectangular field is 360 m.If the width of the field is 85 m, what is its length?

Answers

In order to calculate the length of the rectangular field, you use the following formula for the calculation of the perimeter:

P = 2l + 2w

w: width = 85 m

l: length = ?

P: area = 360m

You know the value of P and w, so, you can solve for l in the formula for the perimeter of the field, just as follow:

P = 2l + 2w

2l = P - 2w

l = (P - 2w)/2

Next, you replace the values of P and w:

l = (360m - 2(85m))/2 = 95 m

Hence, the length of the rectangular field is 95m

Bartlett Electronics pays all sales representatives 4% commission on the first $35,000 of their individual sales and 7% commission on their individual sales in excess of $35,000. Assume that John Morgan sold merchandise valued at $73,500 during the month of November. Calculate the following amounts. (a) Commission on sales in the sales base: $ (b) Commission on additional sales: $ (c) Gross pay:

Answers

As per the given percentage,

a) Commission base in the sales base is $1400

b) Commission on additional sales is $2695

c) Gross pay is $4095.

Percentage:

Percentage is a number or ratio that can be expressed as a fraction of 100.

If we want to calculate percent of a number, divide the number by the whole and multiply by 100.

It can be represented using the symbol (%).

Given,

Bartlett Electronics pays all sales representatives 4% commission on the first $35,000 of their individual sales and 7% commission on their individual sales in excess of $35,000.

John Morgan sold merchandise valued at $73,500 during the month of November.

Here we need to find the following:

a) Commission on sales in the sales base

b) Commission on additional sales

c) Gross pay

a) Commission on sales in the sales base

So, based on the percentage the commission is,

=> 35,000 x 4/100

=> 35,000 x 0.04

=> 1400

b) Commission on additional sales

For this one, first we have to calculate the additional sales amount,

That can be calculated as,

=> 73,500 - 35,000

=> 38,500

Now, the commission is,

=> 38,500 x 7/100

=> 38,500 x 0.07

=> 2695.

c) Now the gross pay for John is,

=> 1400 + 2695

=> 4095

Therefore, the gross pay is $4095.

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an employee at the bank notices an abandoned account with a balance of $360. the bank charges a monthly fee of $8 to maintain an account. the equation for this situation is y = 360 - 8x, where x is the number of months, and y is the balance in dollars. Part A: Find the y-intercept Part B: Find the x-interceptPart C: Interpret the meaning of the x- and y-intercept in terms of the problem.

Answers

Given:

There are given the equation:

[tex]y=360-8x[/tex]

Explanation:

(A):

To find the y-intercept, we need to put 0 for x and solve the equation for the value of y.

So,

From the function:

[tex]\begin{gathered} y=360-8(0) \\ y=360 \end{gathered}[/tex]

Hence, the y-intercept is shown below:

[tex](0,360)[/tex]

(B):

To find the x-intercept, we need to put 0 for y and find the values for x:

So,

[tex]\begin{gathered} y=360-8x \\ 0=360-8x \\ 8x=360 \\ x=\frac{360}{8} \\ x=45 \end{gathered}[/tex]

Hence, the value x-intercept is shown below:

[tex](45,0)[/tex]

(C):

The interpret the meaning of the x- and the y-intercept is shown below:

In the given context, the y-intercept, and x-intercept, mean x = 0 and y = 0 and also refers to the starting values.

For a time-based exercise, this will be the value when we started talking we read or when we started tracking the time and its related changes.

h(r) = (r +1)(r+8)1) What are the zeros of the function?Write the smaller r first, and the larger second.smaller r =larger s 2) What is the vertex of the parabola

Answers

For the zeros of the function, we have to solve h(r)=0, therefore:

[tex]\begin{gathered} h(r)=(r+1)(r+8) \\ h(r)=0 \\ \Rightarrow(r+1)(r+8)=0 \\ \Rightarrow r=-1\text{ or } \\ r=-8 \end{gathered}[/tex]

then, the smaller r is -8 and the larger is -1.

Now, to find the vertex of the parabola, we can find the x-coordinate of the vertex from the general rule:

[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \text{ x-coordinate: -b/2a} \end{gathered}[/tex]

In this case, we have the following:

[tex]\begin{gathered} h(r)=(r+1)(r+8)=r^2+8r+r+8=r^2+9r+8 \\ \Rightarrow a=1,b=9 \\ \Rightarrow-\frac{b}{2a}=-\frac{9}{2(1)}=-\frac{9}{2} \end{gathered}[/tex]

now that we have the x-coordinate of the vertex, we just evaluate the function on that point to find the y-coordinate of the vertex:

[tex]h(-\frac{9}{2})=(-\frac{9}{2}+1)(-\frac{9}{2}+8)=(-\frac{7}{2})(\frac{7}{2})=-\frac{49}{4}[/tex]

therefore, the vertex of the parabola is the point (-9/2,-49/4)

[tex]f(x) = \sqrt{ {x }^{2} - 121} [/tex]what's the inverse of this equation

Answers

EXPLANATION:

The first thing to do in the equation is to interchange the variables in order to do the inverse function and thus solve the equation correctly.

So the equation is as follows:

[tex]\begin{gathered} x=\sqrt[]{x^2-121} \\ Now\text{ we exchange }the\text{ variables x and y;} \\ x=\sqrt[]{y^2-121} \\ y=\sqrt[]{x^2+121};\text{ y}=-\sqrt[]{x^2+121} \\ \sqrt[]{x^2+121\text{ ; }-\sqrt[]{x^2+121}} \\ \text{the answer is : }\sqrt[]{x^2+121\text{ },\text{ }}\text{ }-\sqrt[]{x^2+121^{}} \end{gathered}[/tex]

Determine the angle of rotation if an image is the result of a composition of two reflections across perpendicular lines.

Answers

The angle of rotation if an image is the result of a composition of two reflections across perpendicular lines is 180 degrees

How to determine the angle of rotation of reflection os perpendicular line

Rotation and reflection are forms of transformation as seen in mathematics. The two are related in some forms.

When a reflection is done on a plane perpendicular to the preimage the image is reflected at the perpendicular plane. This is equal to rotation of an angle 90 degrees.

When the reflection is continued again across the perpendicular line, another reflection is noticed and similar rotation however in this case with respect to the initial image, the rotation is now 180 degrees.

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Find the equation of the line that is parallel to the line y = -2x +3 and passes through the point (5,4).y = − 1/2x + 6.5y = 2x - 14y = -2x + 14y = 1/2x + 1.5

Answers

lets remember how to find the equation of a parallel line

two lines are parallel if they don"t intersect, that means they slopes are the same

y=-2x+3

slope as we see is m=-2

the other line has to pass through point (5,4)

y-y1=m(x-x1)

y-4=-2(x-5)

we solve the equation

y= 4-2x+10

y= -2x+14

i will send you a picture

green line is y=-2x+14

Identify the rate of change and Intial Value in this equationy = 3x +6

Answers

The rate of change is 3.

The initial value is 6.

Step - by - Step Explanation

What to find?

• Rate of change.

,

• Initial value.

Given:

y = 3x + 6

The rate of change is also the same as the slope.

To find the slope of the gien equation, compare the equation with y=mx + b.

Where m is the slope (rate of change).

Comparing the two equations, m = 3

Hence, the rate of change is 3.

The initial value also known as the y-intercept, is the value of y at x=0.

y = 3(0) + 6

y = 6

Hence, the initial value is 6.

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