Question 653189
You are told the speed of the bullet is dependent on the distance from the gun. When the gun is fired, the bullet has some speed at a distance of 0. Let us call that initial speed S(0) (Speed at Distance of 0). We want to create an equation that gives the speed at any given distance after the gun is fired. 

{{{S(t) = S(0) + mD(t)}}}

Now we need to use the given information to find m and S(0). m is the slope. Since we are told the equation is linear and we are given two data points, we can calculate the slope m.

{{{m = (2600-3500)/(250-25)}}} 
{{{m = -900/225}}}
{{{m = -4}}}

A negative slope makes sense since the bullet is slowing down as the distance increases.

So we have m, let's plug that in
{{{S(t) = S(0) - 4*D(t)}}}

Now use either one of the given data points and plug that in. Then solve for S(0)

{{{3500 = S(0) - 4*25}}}
{{{3500 = S(0) - 100}}}
{{{3600 = S(0)}}}

So plug that in
{{{S(t) = 3600 - 4*D(t)}}}
Test that against the two data points we know. Does it yield 3500 at 25 and 2600 at 250? Check it out

Now you know the equation. So use it to solve parts B through D. For B plug in d(t) = 300 and solve for S(t). For C, plug in S(t)=500 and solve foe D(t).
For D, D(t) = 0. 

For E, S(t)=0

For F, we already solved for m in the beginning. What does m mean? It gives the rate the speed slows per foot traveled.