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?
Line l could be represented by the equation y=3x.
This line passes through the origin and has a positive slope, indicating that it extends into both quadrant I and quadrant III while avoiding quadrants II and IV, aligning with the given conditions.
This equation represents a vertical line that crosses the x-axis at x=3. Such a line would exist entirely in quadrants I and IV, failing to meet the requirement of not containing points in quadrant IV.
This equation describes a line with a positive slope that passes through the origin (0,0). As it moves upwards to the right, it remains entirely in quadrants I and III, thus avoiding both quadrants II and IV, making it a valid option for line l.
This equation represents a line parallel to y=3x but shifted upwards by 3 units. While it still has a positive slope, it crosses the y-axis at (0,3) and does extend into quadrant II, which disqualifies it from being a suitable equation for line l.
This line has a negative slope and crosses the y-axis at (0,-3). It extends into quadrants II and IV, specifically entering quadrant IV as it moves downward, making it incompatible with the condition of not containing points in either of these quadrants.
The equation y=3x best meets the criteria outlined in the question, as it lies solely within quadrants I and III. The other options either extend into quadrants II or IV or do not adhere to the specified restrictions. Thus, line l is correctly represented by the equation y=3x.
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