Slope of line
m= (y2-y1)/(x2-x1)
=(-4--6)/(6--2)
=2/8
=1/4
Line in two point form
(y-y1)=m(x-x1)
y--2=(1/4)(x-6)
y+2=(1/4)(x-6)
simplify
4(y+2)=x-6 =>
x-4y-14=0
Alternatively, use the slope intercept form:
y--2=(1/4)(x-6) =>
y=(1/4)x - 3/2-2 =>
y=(1/4)x -7/2
H1 (t) = 196 - 16 t-squared. / / / H2 (t) = 271-16t-squared. / / / In each function, 't' is the number of seconds after that ball is dropped. / / / Each function is only true until the first time that H=0, that is, until the first bounce. Each function becomes very complicated after that, and we would need more information in order to write it.
Answer:
Therefore the rate change of height is
m/s.
Step-by-step explanation:
Given that a vertical cylinder is leaking water at rate of 4 m³/s.
It means the rate change of volume is 4 m³/s.

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.
The height of the cylinder be h(say).
The volume of a cylinder is 


Differentiating with respect to t.

Putting the value 



The rate change of height does not depend on the height.
Therefore the rate change of height is
m/s.