Algebra I Unit 4C CBA 2024-2025 [15 Items] 12. Which ordered pair is in the solution set of ygeqslant (1)/(3)x+4

To determine which ordered pair is in the solution set of the inequality \( y \geq \frac{1}{3}x + 4 \), we need to check if the y-coordinate of each ordered pair is greater than or equal to the value of \( \frac{1}{3}x + 4 \) for the corresponding x-coordinate.<br /><br />Let's consider the following ordered pairs:<br />A. (0, 5)<br />B. (3, 6)<br />C. (6, 3)<br />D. (9, 2)<br /><br />We will substitute the x and y values of each ordered pair into the inequality \( y \geq \frac{1}{3}x + 4 \) and check if the inequality holds true.<br /><br />A. For the ordered pair (0, 5):<br />\( 5 \geq \frac{1}{3}(0) + 4 \)<br />\( 5 \geq 4 \)<br />This is true, so the ordered pair (0, 5) is in the solution set.<br /><br />B. For the ordered pair (3, 6):<br />\( 6 \geq \frac{1}{3}(3) + 4 \)<br />\( 6 \geq 1 + 4 \)<br />\( 6 \geq 5 \)<br />This is true, so the ordered pair (3, 6) is in the solution set.<br /><br />C. For the ordered pair (6, 3):<br />\( 3 \geq \frac{1}{3}(6) + 4 \)<br />\( 3 \geq 2 + 4 \)<br />\( 3 \geq 6 \)<br />This is false, so the ordered pair (6, 3) is not in the solution set.<br /><br />D. For the ordered pair (9, 2):<br />\( 2 \geq \frac{1}{3}(9) + 4 \)<br />\( 2 \geq 3 + 4 \)<br />\( 2 \geq 7 \)<br />This is false, so the ordered pair (9, 2) is not in the solution set.<br /><br />Therefore, the ordered pairs in the solution set of the inequality \( y \geq \frac{1}{3}x + 4 \) are (0, 5) and (3, 6).