Question

Which quadrants contain the points of the graph 2x - y > 4?"

a) Quadrants I and II
b) Quadrants II and III
c) Quadrants III and IV
d) Quadrants I and IV

Answer 1

Quadrants II and IV contain the points of the graph 2x - y > 4.

Step-by-step explanation:

The graph of the inequality 2x - y > 4 represents a region in the coordinate plane. To determine which quadrants contain the points in this region, we need to examine the signs of the x and y components of the points.

1. If we choose a point in Quadrant I (both x and y positive), we can substitute its coordinates into the inequality to see if it is true. For example, if we choose (2, 3), we have 2(2) - 3 > 4, which is false. Therefore, Quadrant I does not contain any points of the graph.
2. If we choose a point in Quadrant II (x negative, y positive), we can substitute its coordinates into the inequality to see if it is true. For example, if we choose (-2, 3), we have 2(-2) - 3 > 4, which is true. Therefore, Quadrant II contains points of the graph.
3. If we choose a point in Quadrant III (both x and y negative), we can substitute its coordinates into the inequality to see if it is true. For example, if we choose (-2, -3), we have 2(-2) - (-3) > 4, which is false. Therefore, Quadrant III does not contain any points of the graph.
4. If we choose a point in Quadrant IV (x positive, y negative), we can substitute its coordinates into the inequality to see if it is true. For example, if we choose (2, -3), we have 2(2) - (-3) > 4, which is true. Therefore, Quadrant IV contains points of the graph.

Based on these calculations, the quadrants that contain the points of the graph 2x - y > 4 are Quadrants II and IV.