Answer:
Intersept is (4.55,0)
Step-by-step explanation:
The maximum height is 64ft and the ballon is only in the air for 2 seconds
8 feet, because 10^{2} - 6^{2} = 64;
\sqrt{64} = 8[tex]
The slope-intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (-3, 1) and (2, -4). Substitute:
![m=\dfrac{-4-1}{2-(-3)}=\dfrac{-5}{5}=-1](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-4-1%7D%7B2-%28-3%29%7D%3D%5Cdfrac%7B-5%7D%7B5%7D%3D-1)
Therefore we have the equation of a line
![y=-1x+b\to y=-x+b](https://tex.z-dn.net/?f=y%3D-1x%2Bb%5Cto%20y%3D-x%2Bb)
Put the coordinates of the point (-3, 1) to the equation:
![1=-(-3)+b](https://tex.z-dn.net/?f=1%3D-%28-3%29%2Bb)
<em>subtract 3 from both sides</em>
![-2=b\to b=-2](https://tex.z-dn.net/?f=-2%3Db%5Cto%20b%3D-2)
<h3>Answer: y = -x - 2</h3>