Question

determine whether the following statement is true or false. when graphing 3x - 4y ≥ 2, to determine which side of the line to shade, choose a test point on 3x - 4y = 2. choose the correct answer below. a. the statement is false. the test point should be chosen from one of the half-planes. b. the statement is true. the test point should always be on the line. c. the statement is true. it does not matter where the test point is chosen. d. the statement is false. the test point should always be chosen to match the inequality.

Explanation:

To determine the shaded region for \(3x - 4y \geq 2\), we test a point not on the line (since the line \(3x - 4y = 2\) is part of the solution for \(\geq\), but test points for shading are chosen from one of the half - planes (regions divided by the line), not on the line itself). The statement says to choose a test point on \(3x - 4y = 2\), which is incorrect. Option A correctly states that the statement is false and that the test point should be chosen from one of the half - planes. Option B is wrong because test points for shading (to determine the half - plane) are not on the line. Option C is wrong as the choice of test point matters (it should be off the line, in a half - plane). Option D's reasoning is incorrect as the test point is used to see if it satisfies the inequality, not "match" it in that way.

Answer:

A. The statement is false. The test point should be chosen from one of the half - planes.