Ineed some on this asap .

the table shows the outputs y for different inputs x:

input
(x)
5 6 7 8

output
(y)
2 5 8 11

part a: do the data in this table represent a function? justify your answer.
part b: compare the data in the table with the relation f(x) = 2x + 13. which relation has a greater value when x = 7?
part c: using the relation in part b, what is the value of x if f(x) = 75?

Part A: In the given problem we have given values of x and values of y.

Part B: f(x) = 2x + 13 has greater value at x= 7

Part C: The value of x is 31.

One key point to observe is that for each x there is a unique y hence the given data belongs to a function but the equation of this function is not known.

Let us fit a line into the given data of x and y which can be given by the formula:

  ....(1)

Putting the values from data in equation (1)

we get y-2= ((5-2)/(6-5)) (x-5)

(Taking first two points for instance)

y-2 = 3( x- 5) y= 3x-13     ....(2)

Part B : Another function is given in the question is

f(x) = 2x +13 ....(3)

Now, we can find out the values of equation (2) and equation (3) for x= 7.

Putting in equation (2) we can get y(7) = 21-13 = 8.

Similarly,

f(7) = 2 7 + 13 f(7) = 14 +13 = 27

so we can conclude that equation (3) has a greater value at x =7.

Part C :

Using the relation that is concluded in Part B

75 = 2x +13

75-13= 2x

62 = 2x

x = 31

Thus, the value of x is 31.

For more information please refer to the link below:

link

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i believe that the slope of the line is -5

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