Coordinate Geometry - Gradient of a Straight Line

A band compares two rehearsal studios. Each studio charges a booking fee plus an hourly rate. Booking durations may include fractions of an hour.
The graph shows the total charge, \(C\) dollars, for a booking lasting \(t\) hours.

1. Calculate the gradient of Studio Echo’s line.

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2. Explain what this gradient represents in this situation.

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3. Write an equation connecting \(C\) and \(t\) for Studio Echo.

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4. Using the graph, estimate how much the band saves by choosing Studio Echo instead of Studio Pulse for a \(7.5\)-hour booking.

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5. A band member says, “Studio Pulse has a smaller booking fee, so it is cheaper for every booking.” Is this correct? Justify your answer using the graphs.

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