Answer: You are incorrect, the slope is correct, but the actual y-intercept is 205 ft.
Then the equation is:
y = (-15 ft/min)*x + 205 ft
Step-by-step explanation:
Ok, let's solve this.
We know that water is drained from a reservoir, let's assume that we can model this situation with a linear relation:
y = a*x + b
Where x is time, y is the height of the water in the reservoir, a is the slope (in this case represents how much changes the height of the water in the reservoir in one unit of time) and b is the initial height of the water in the reservoir.
We know that for a line that passes through the points (x₁, y₁) and (x₂, y₂) the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
For this particular case we know that after 2 minutes the height of the water is 175 ft, then we have the point (2 min, 175 ft)
and after 5 minutes (so 7 minutes in total), the height of the water is 100ft, then: (7 ft, 100ft)
Then the slope of this:
a = (100 ft - 175 ft)/(7 min - 2 min) = (-75ft/5min) = - 15 ft/min
Then our line is something like:
y = (-15ft/min)*x + b
To find the value of b, we can use the fact that when x = 2 min, y = 175 ft
So if we replace these two values in the equation we get:
175ft = (-15 ft/min)*2 min + b
175 ft = -30 ft + b
175 ft + 30 ft = b
(here is your problem, it seems like you subtracted instead of adding in this part)
205 ft = b
Then the equation is:
y = (-15 ft/min)*x + 205 ft
So you are incorrect (but only for a little bit), you computed wrong the y-intercept.
and 
. Then we want to find the exact value of 
.
. By the Pythagorean theorem, we also find 
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
, then (by Pythagorean theorem) 
, so 
. And from this, 
.
