Question

Help, pleeeease! A plane is on its approach to land on the runway. The jet’s height above the ground is given in feet as a function of the time in seconds. The following table tracks the plane as it lands:

t (in seconds) h (in feet)
0                           4000
5                            3500
10                           3000
15                           2500
20                            2000
25                          1500
Is this function linear? If it is, what is the slope? Use the formula m= △h/△t

Answer 1

The answer is (0, 40); The jet lands in 40 seconds.

Answer 2

The function is linear

Slope is -100

Explanation:

Given :

t (in seconds) h (in feet)

0 4000

5 3500

10 3000

15 2500

20 2000

25 1500

Solution:

To check whether the function is linear or not we will use two point slope form:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`(x_1,y_1)=(0,4000)`

`(x_2,y_2)=(5,3500)`

Now substitute the values

`y-4000=(3500-4000)/(5-0)(x-0)`

`y-4000=(-500)/(5)(x-0)`

`y-4000=-100(x-0)`

`y-4000= -100x`

Now check the given points ,whether they satisfies the obtained equation:

(10,3000)

`3000-4000= -100(10)`

`-1000= -1000`

Hence satisfied

Thus the function is linear :
`y-4000= -100x`

Now to find slope:
`m= \frac{\Delta{h}}{\Delta{t}}`

`\Delta {h} = h_2-h_1`

`\Delta {h} = 3500-4000`

`\Delta {h} = -500`

`\Delta {t} = t_2-t_1`

`\Delta {t} =5-0`

`\Delta {t} = 5`

So,
`m= (-500)/(5)`

`m= -100`

Hence the slope is -100