Answer:
S = -90t + 550
Explanation:
First we must note a few key things the question tells us:
1. The tickets sell at a constant rate, thus implying a linear relationship.
2. Tickets start selling at 10
3. The independent variable (t) is in hours after 10
4. The number of tickets (S) is declining, thus we should expect a negative gradient.
5. The number of tickets is our dependent variable since it is reliant on time.
y = mx+c is our general linear expression which we will call "Eq 0"
Lets substitute our knowns into this to find m and c. We know that "t" is independent and that "S" is dependent on "t" therefore, we know that our x-axis will be representing values for "t" and that our y-axis will represent values for "S"
We must use simultaneous equations to find m and c
Eq 1: 550 = m(0) + c -> 550 = c
Eq 2: 280 = m(3) + c -> 280 = 3m + c
From Eq 1. we already know that our y intercept is at 550.
To find our gradient, we must substitute our known (550 being the y-intercept) into the next equation.
Thus,
280 = 3m + 550
To isolate our variable (m) we subtract both sides by 550
280 - 550 = 3m + 550 - 550
-270 = 3m
To finally find m, we divide both sides by 3
-270/3 = 3m/3
-90 = m
Now we substitue both our knows into Eq 0, note that our gradient (m) is negative as expected.
y = -90x + 550
Or, in terms of S and t
S = -90t + 550