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Determine the equations of the straight line and the parabola shown in the graph.

Mathematics

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Step 1: Identify known points and functions.
From the graph:

  • The straight line passes through P and E.
  • P is the y-intercept of the line. From the markings, P is at $(0, 4)$.
  • E is the x-intercept of the line. From the markings, E is at $(2, 0)$.
  • The parabola passes through the origin O $(0, 0)$.
  • Point N is on the parabola, with an x-coordinate of 1. From the graph, its y-coordinate appears to be 1. So, N $(1, 1)$.
  • Point M is on the parabola, with a y-coordinate of -2.
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