22. In the xy- coordinate system above, line l (not shown) does not contain points in either quadrant II or quadrant IV. Which of the following could be the equation of line l?
Answer: B
Line l could be the equation y=3x.
The equation of line l that does not contain points in either quadrant II or quadrant IV must have a positive slope and must lie in quadrants I and III. The equation y=3x meets this criterion as it is a straight line that passes through the origin and has a positive slope.
A) x=3
This equation represents a vertical line that crosses the x-axis at x=3. This line includes points from both quadrant I and quadrant II, as it does not restrict itself to only quadrants I and III, making it an incorrect option.
B) y=3x
This equation defines a line with a positive slope that passes through the origin. It only includes points from quadrants I and III, which aligns perfectly with the requirement that line l does not contain points in either quadrant II or quadrant IV.
C) y=3x+3
While this line has a positive slope, it crosses the y-axis at (0, 3), which keeps part of the line above the x-axis. This means it also extends into quadrant II, thus failing the requirement that line l does not contain points in that quadrant.
D) y=−3x−3
This equation represents a line with a negative slope that passes through the point (0, -3) and extends into quadrants III and II. Since it intersects quadrant II, it does not satisfy the conditions set for line l.
Conclusion
The equation y=3x is the only option that fulfills the requirement of being limited to quadrants I and III without intersecting quadrants II or IV. All other options either extend into quadrant II or do not fit the criteria of having a positive slope, confirming that B is the valid choice for line l.