Math Problem Statement
find the angle between the lines
6x−y−11=0and7x−y−1=06x−y−11=0and7x−y−1=0
and sketch the graph.
Solution
The graph above shows the two lines:
- (in blue), which has a slope of 6.
- (in red), which has a slope of 7.
The lines intersect at an angle of approximately .
Would you like further details on the solution? Here are some related questions:
- How do slopes affect the angle between two lines?
- What happens if two lines have the same slope?
- How is the tangent function used in calculating angles?
- What is the significance of negative slopes in angle calculations?
- 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