Questions: The graph of 4x+5y=20 is shown on the grid. Which points are in the solution set of 4x+5y<20? Select two correct answers.

The graph of 4x+5y=20 is shown on the grid. Which points are in the solution set of 4x+5y<20? Select two correct answers.
Transcript text: The graph of $4 x+5 y=20$ is shown on the grid. Which points are in the solution set of $4 x+5 y<20$ ? Select two correct answers.
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Solution

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Solution Steps

Step 1: Identify the points

The points we are given to check are (-2, 4), (1, 4), (0, 4), (4, -1), and (5, 0).

Step 2: Test the given points

We plug each point's coordinates into the inequality $4x + 5y < 20$:

  • (-2, 4): 4(-2) + 5(4) = -8 + 20 = 12 < 20. This point is in the solution set.

  • (1, 4): 4(1) + 5(4) = 4 + 20 = 24 > 20. This point is not in the solution set.

  • (0, 4): 4(0) + 5(4) = 0 + 20 = 20. This point is not in the solution set since the inequality is strictly less than.

  • (4, -1): 4(4) + 5(-1) = 16 - 5 = 11 < 20. This point is in the solution set.

  • (5, 0): 4(5) + 5(0) = 20 + 0 = 20. This point is not in the solution set.

Final Answer: The points (-2, 4) and (4, -1) are in the solution set.

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