Question

Tickets for a show go on sale at 10:00AM and sell at a constant rate. The table below

shows the number of tickets sold (S) as a function of time (t).
t (time, in hours,
since 10AM)
S (show tickets)
0
550
3
280
5
100

Answer 1

The equation expressing
`\( S \)` as a function of
`\( t \)` is
`\( S(t) = -90t + 550 \)`.

To find an equation expressing
`\( S \)` (number of show tickets sold) as a function of
`\( t \)` (time in hours since 10:00 AM), we can use linear interpolation between the given points
`\((0, 550)\)`,
`\((3, 280)\), and \((5, 100)\)`.

The equation of a line can be written in the form
`\(y = mx + b\)`, where
`\(m\)` is the slope and
`\(b\)` is the y-intercept.

1. Find the slope
`\(m\)` using the formula
`\(m = \frac{\text{change in } y}{\text{change in } x}\):`

`\[ m = (280 - 550)/(3 - 0) = (-270)/(3) = -90 \]`

2. Now, use the point-slope form of a line
`(\(y - y_1 = m(x - x_1)\))` with one of the given points, let's say
`\((0, 550)\)`:

`\[ y - 550 = -90(x - 0) \]`

3. Simplify the equation:

`\[ y = -90x + 550 \]`

So, the equation expressing
`\( S \)` as a function of
`\( t \)` is
`\( S(t) = -90t + 550 \)`.

The probable question is attached below.