Answer:
To determine which graph represents the system of linear inequalities y ≤ 1/3x - 6 and y ≤ -1/2x - 1, we need to analyze the slopes and y-intercepts of the two inequalities.
The first inequality, y ≤ 1/3x - 6, has a slope of 1/3 and a y-intercept of -6. This means that the line will be relatively steep, and it will intersect the y-axis at -6.
The second inequality, y ≤ -1/2x - 1, has a slope of -1/2 and a y-intercept of -1. This line will have a negative slope and intersect the y-axis at -1.
Now, let's compare these characteristics with the graphs provided:
- The first graph has a steep line with a negative y-intercept. However, the slope does not match the first inequality.
- The second graph has a line with a negative slope, and its y-intercept matches the second inequality.
- The third graph has a line with a positive slope, which does not match either of the inequalities.
- The fourth graph has a line with a negative slope and a y-intercept that matches the second inequality.
Based on this analysis, the second graph represents the system of linear inequalities y ≤ 1/3x - 6 and y ≤ -1/2x - 1.
Explanation: