Determine whether each inequality is represented by Graph 1 or Graph 2. Select Graph 1 or Graph 2 for each inequality.
Graph 1
Graph 2
y < –x + 3
x + y < 3
6 < 2x + 2y
–y > x – 3
To determine whether each inequality is represented by Graph 1 or Graph 2, we need to compare the inequalities with the equations represented by the graphs. Here's how we can do it:
1. Graph 1 represents a line where y is less than –x + 3. The slope-intercept form of this line is y = –x + 3. So, any point that lies below this line on Graph 1 satisfies the inequality y < –x + 3.
2. Graph 2 represents a line where x + y is less than 3. The slope-intercept form of this line is y = –x + 3, similar to the first equation. However, the inequality differs. In this case, any point that lies below this line on Graph 2 satisfies the inequality x + y < 3.
3. Graph 1 does not represent the inequality 6 < 2x + 2y. To determine which graph represents this inequality, we need to rewrite it in slope-intercept form. Dividing both sides of the inequality by 2, we get 3 < x + y. This is the same equation as in the second graph, so Graph 2 represents the inequality 6 < 2x + 2y.
4. Finally, Graph 1 represents the inequality –y > x – 3. To determine which graph represents this inequality, we need to rewrite it in slope-intercept form. Dividing both sides of the inequality by -1, we get y < -x + 3. This matches the equation for Graph 1, so Graph 1 represents the inequality –y > x – 3.
Summary:
- Graph 1 represents the inequalities y < –x + 3 and –y > x – 3.
- Graph 2 represents the inequalities x + y < 3 and 6 < 2x + 2y.