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
