Coordinate Geometry - Gradient of a Straight Line

A school is choosing between two sponsorship offers for a charity walk. Each sponsor offers a fixed donation plus an additional amount for every kilometre completed.
The graph shows the total donation, \(D\) dollars, for a completed distance of \(x\) kilometres.

1. Calculate the gradient of Sponsor Gold’s line.

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2. Explain what this gradient represents in this situation.

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3. Write an equation connecting \(D\) and \(x\) for Sponsor Gold.

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4. Using the graph, estimate how much more money the school receives from Sponsor Gold than from Sponsor Green if \(16\) km is completed.

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5. The final distance will be between \(8\) km and \(14\) km. A student says, “We should choose Sponsor Gold because its donation increases faster.” Explain why this information is insufficient to guarantee that Gold gives the larger donation.

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