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jek_recluse [69]
3 years ago
11

The slope of a line that passes through points (5, 14) and (-4, y) is 4/9. What is the value of y?​

Mathematics
2 answers:
Alex777 [14]3 years ago
4 0

Answer: y = 10

Step-by-step explanation:

The slope of a line is the rise/run, so if you want to find the slope of a line between two points, you can take the change in y between the two points and divide it by the change in x.

The change in y would be (y2 - y1), where y2 is the y position of the second point and y1 is the y position of the first.

In a similar manner, to find the change in x, we can use (x2 - x1), where x2 is the x position of the second point and x1 is the x position of the first.

Now that we have the change in x and the change in y, we can make an equation to find the slope (which is change in y / change in x):

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

Now we can assign the points:

Point 1 is (5, 14)

Point 2 is (-4, y)

(Note: You could flip which point is which, and it wouldn't change the final answer, I'm just assigning these so you know where the x and y values are coming from when I plug the values into the equation)

Now that we have both points, we can plug the values into the equation:

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

m = (y - 14) / (-4 - 5)

m = (y - 14) / (-9)

There's one piece of information we haven't used yet, which will help us solve for the value of y. What we need to use is the slope (which is given to us as 4/9).

Plugging in the value of the slope will let us get y:

m = (y - 14) / (-9)

4/9 = (y - 14) / (-9)

-4 = (y - 14)

(Note: We're multiplying both sides by -9, don't forget about the negative sign)

-4 = y - 14

y = -4 + 14

y = 10

Monica [59]3 years ago
3 0

Answer:

slope=m=4/9

(x',y')=(5,14)

(x",y")=(-4,y)

we have

m=(y"-y')/(x"-x')

4/9=(-4-5)/(y-14)

4y-56=-81

4y=-81+56

y=-25/4

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Amanda went to the store to purchase ink pens. She found three kinds of pens. The first cost $4 each; the price of the second ki
KonstantinChe [14]

Answer:

Amanda buy first kind of pen = 3

Amanda buy second kind of pen = 2

Amanda buy third kind of pen = 15

Step-by-step explanation:

Given - Amanda went to the store to purchase ink pens. She found three    

            kinds of pens. The first cost $4 each; the price of the second kind

            was 4 for $1; and the cost for the third kind was 2 for $1. She bought

            20 pens and she bought at least one of each kind. (It is possible to

            buy only 1 of the pens that are "4 for $1" or "2 for $1".) The cost was

            $20.

To find - When she got back to her office, Amanda decided to turn this into

              a math problem for me. She asked: how many of each kind did I

              buy?

Proof -

Let Amanda buy first kind of pen = x

                      second kind of pen = y

                           third kind of pen = z

As given,

She bought total pen = 20

⇒x + y + z = 20          ...............(1)

Now,

As given,

cost for first kind pen = $4 for 1 pen

As she bought x pens of first kind , so

Cost of x pens of first kind = $4x

Now,

The price of the second kind was 4 for $1

⇒Cost of second kind = $\frac{1}{4} for 1 pen

As she bought y pens of send kind , so

Cost of y pens of second kind = $\frac{1}{4}y

Now,

The price of the third kind was 2 for $1

⇒Cost of third kind = $\frac{1}{2} for 1 pen

As she bought z pens of send kind , so

Cost of z pens of third kind = $\frac{1}{2}z

Now,

As given, The cost was $20

⇒4x + \frac{1}{4}y + \frac{1}{2}z = 20

⇒16x + y + 2z = 80             .....................(2)

∴ we get 2 equations

x + y + z = 20                   .....................(1)

16x + y + 2z = 80             .....................(2)

Now,

Subtract equation (1) from equation (2) , we get

16x + y + 2z  - ( x+ y + z )= 80 - 20

⇒16x + y + 2z - x - y - z = 60

⇒15x + z = 60

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Now,

Put the value of z in equation (1) , we get

x + y + 60 - 15 x = 20

⇒ y - 14x = 20 - 60

⇒y - 14x = -40

⇒14x - y = 40

⇒y = 14x - 40

Now,

we get

z = 60 - 15x

y = 14x - 40

As given

she bought at least one of each kind

it means x > 1, y > 1, z > 1

Now,

If x = 1, then y = 14 - 40 = -26

Not possible

If x = 2 , then y = 14(2) - 40 = -12

Not possible

If x = 3, then y = 14(3) - 40 = 2 and z = 60 - 15(3) = 15

Possible.

If x = 4,  then y = 14(4) - 40 = 16 and z = 60 - 15(4) = 0

Not Possible.

If x = 5, then y = 14(5) - 40 = 30 and z = 60 - 15(5) = -15

Not Possible.

∴ we get

x = 3, y = 2, z = 15

Amanda buy first kind of pen = x = 3

Amanda buy second kind of pen = y = 2

Amanda buy third kind of pen = z = 15

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Answer:

Option 1 - Using the Subtraction Property of Equality, 2 is subtracted from both sides of the equation.          

Step-by-step explanation:

Given : Process

Step 1: 4x + 2 = 10

Step 2: 4x = 8

To find : Which justification describes the process?

Solution :

From step 1 to step 2, we subtract 2 both sides

Step 1: 4x + 2 = 10

Subtracting 2 both side,

⇒ 4x + 2-2 = 10-2

Step 2: 4x = 8

So, The best justification is 'Using the Subtraction Property of Equality, 2 is subtracted from both sides of the equation'.

Therefore, Option 1 is correct.

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