To plot the graph representing the number of T-shirts Sherry has left to sell, we can follow these steps:
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Identify Variables:
- Let \( x \) represent the number of days since Sherry started selling.
- Let \( y \) represent the number of T-shirts left.
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Initial Condition:
- At \( x = 0 \) (when she starts selling), \( y = 40 \).
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Selling Rate:
- Sherry sells 5 T-shirts each day, so her supply decreases linearly.
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Equation of the Line: The equation for the number of T-shirts left can be expressed as: \[ y = 40 - 5x \]
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Determine When T-shirts Run Out:
- Set \( y = 0 \) to find out how many days it takes to sell all T-shirts: \[ 0 = 40 - 5x \Rightarrow 5x = 40 \Rightarrow x = 8 \] Sherry will run out of T-shirts in 8 days.
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Plot the Points:
- At \( x = 0 \): \( y = 40 \) (initial T-shirts)
- At \( x = 1 \): \( y = 40 - 5(1) = 35 \)
- At \( x = 2 \): \( y = 40 - 5(2) = 30 \)
- At \( x = 3 \): \( y = 40 - 5(3) = 25 \)
- At \( x = 4 \): \( y = 40 - 5(4) = 20 \)
- At \( x = 5 \): \( y = 40 - 5(5) = 15 \)
- At \( x = 6 \): \( y = 40 - 5(6) = 10 \)
- At \( x = 7 \): \( y = 40 - 5(7) = 5 \)
- At \( x = 8 \): \( y = 40 - 5(8) = 0 \)
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Graph:
- On the x-axis (days): from 0 to 8.
- On the y-axis (T-shirts left): from 0 to 40.
- Plot the points: (0,40), (1,35), (2,30), (3,25), (4,20), (5,15), (6,10), (7,5), (8,0).
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Draw the Line:
- Connect the points with a straight line.
The resulting graph would show a linear decline in the number of T-shirts from 40 down to 0 over the span of 8 days, with a slope of -5 (downwards) indicating she sells 5 T-shirts per day.
Summary of the Graph
- X-Axis: Days (0 to 8)
- Y-Axis: T-shirts left (0 to 40)
- Line: Starts at (0, 40) and ends at (8, 0) with a linear slope representing the number of T-shirts sold each day.
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