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:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(0,4000)[/tex]
[tex](x_2,y_2)=(5,3500)[/tex]
Now substitute the values
[tex]y-4000=\frac{3500-4000}{5-0}(x-0)[/tex]
[tex]y-4000=\frac{-500}{5}(x-0)[/tex]
[tex]y-4000=-100(x-0)[/tex]
[tex]y-4000= -100x[/tex]
Now check the given points ,whether they satisfies the obtained equation:
(10,3000)
[tex]3000-4000= -100(10)[/tex]
[tex]-1000= -1000[/tex]
Hence satisfied
Thus the function is linear : [tex]y-4000= -100x[/tex]
Now to find slope: [tex]m= \frac{\Delta{h}}{\Delta{t}}[/tex]
[tex]\Delta {h} = h_2-h_1[/tex]
[tex]\Delta {h} = 3500-4000[/tex]
[tex]\Delta {h} = -500[/tex]
[tex]\Delta {t} = t_2-t_1[/tex]
[tex]\Delta {t} =5-0[/tex]
[tex]\Delta {t} = 5[/tex]
So, [tex]m= \frac{-500}{5}[/tex]
[tex]m= -100[/tex]
Hence the slope is -100
