Math Problem Statement

find the angle between the lines

6x−y−11=0and7x−y−1=06xy−11=0and7xy−1=0

and sketch the graph.

Solution

The graph above shows the two lines:

  1. 6xy11=06x - y - 11 = 0 (in blue), which has a slope of 6.
  2. 7xy1=07x - y - 1 = 0 (in red), which has a slope of 7.

The lines intersect at an angle of approximately 1.331.33^\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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Analytical Geometry
Slopes of Lines
Angles Between Lines

Formulas

Slope-intercept form of a line: y = mx + b
Formula for the angle between two lines: tan(θ) = |(m2 - m1) / (1 + m1 * m2)|

Theorems

Angle between two lines theorem

Suitable Grade Level

Grades 9-12