find the angle between the lines

6x−y−11=0and7x−y−1=06*x*−*y*−11=0and7*x*−*y*−1=0

and sketch the graph.

The graph above shows the two lines:

1. \( 6x - y - 11 = 0 \) (in blue), which has a slope of 6.
2. \( 7x - y - 1 = 0 \) (in red), which has a slope of 7.

The lines intersect at an angle of approximately \( 1.33^\circ \).

Would you like further details on the solution? Here are some related questions:

1. How do slopes affect the angle between two lines?
2. What happens if two lines have the same slope?
3. How is the tangent function used in calculating angles?
4. What is the significance of negative slopes in angle calculations?
5. How would parallel and perpendicular lines affect the angle formula?

**Tip**: In geometry, the smaller the difference in slopes, the smaller the angle between two lines.

find the angle between the lines 6x−y−11=0 and 7x−y−1=0 and sketch the graph.

This problem demonstrates how to find the angle between the two lines 6x−y−11=0 and 7x−y−1=0, with a step-by-step solution. It covers important algebraic and geometric concepts such as slopes and the angle between two lines. Suitable for students in Grades 9-12.

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