find the angle between the lines x+y+1=0 and 2x-y-1=0. sketch the graph

The graph above shows the two intersecting lines \(x + y + 1 = 0\) and \(2x - y - 1 = 0\), along with the angle between them, which is approximately \(71.57^\circ\).

Let me know if you'd like any further details or clarifications.

Here are some related questions to expand on this topic:
1. How do you determine if two lines are parallel or perpendicular?
2. What is the meaning of the slope in the context of a graph?
3. How would the graph change if one of the slopes were modified?
4. How can you calculate the distance between a point and a line?
5. What is the geometric significance of the y-intercepts in this case?

**Tip:** When two lines are perpendicular, the product of their slopes is always \(-1\).

Find the angle between the lines x+y+1=0 and 2x-y-1=0. Sketch the graph.

Learn how to find the angle between the lines x + y + 1 = 0 and 2x - y - 1 = 0 using the formula for the angle between two lines. This problem covers key concepts in analytic geometry, including linear equations and slopes, suitable for students in Grades 10-12.

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