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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

1 Answer

3 votes

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.

Tickets for a show go on sale at 10:00AM and sell at a constant rate. The table below-example-1
User Paul Lehn
by
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