exam Maths Puzzle Numerical Ability

Why do intersecting lines represent a unique solution? Give examples to support your answer.

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I need help with this problem. Thank you.

Determine the linear function whose graph is a line that parallel to the line g(x)=-3x-4 and contains the point (2,7). need to formulate a conjecture for the series

L = 1^k + 2^k + 3^k +...+ n^k

^ = to the power of

thanks.