Answer:
(a) x = -6: a vertical line passing through (-6, y) for any value of y.
(b) y = 6: a horizontal line passing through (x, 6) for any value of x.
(c) 0 ≤ x: all points to the right of or on the y-axis, but not to the left of the y-axis.
Explanation:
(a) x = -6:
- The equation x = -6 represents a vertical line passing through the point (-6, y) for any value of y. This means that for every value of y, there is a corresponding point on the line that has an x-coordinate of -6. The line is parallel to the y-axis and does not intersect the x-axis.
(b) y = 6:
- The equation y = 6 represents a horizontal line passing through the point (x, 6) for any value of x. This means that for every value of x, there is a corresponding point on the line that has a y-coordinate of 6. The line is parallel to the x-axis and does not intersect the y-axis.
- (c) 0 ≤ x:
- The inequality 0 ≤ x represents all points to the right of the y-axis, including the points on the y-axis. This is because the x-coordinate of any point to the right of the y-axis is positive or zero, while the x-coordinate of any point to the left of the y-axis is negative. The inequality excludes the points to the left of the y-axis, which have negative x-coordinates. Therefore, the set of all points P(x, y) where 0 ≤ x is the set of all points to the right of or on the y-axis, but not to the left of the y-axis.