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

Answer:

The function is linear

Slope is -100

Step-by-step 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:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

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

Now substitute the values

$y-4000=\frac{3500-4000}{5-0}(x-0)$

$y-4000=\frac{-500}{5}(x-0)$

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

$y-4000= -100x$

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,  $m= \frac{-500}{5}$

$m= -100$

Hence the slope is -100