Math Problem Statement
find the angle between the lines x+y+1=0 and 2x-y-1=0. sketch the graph
Solution
The graph above shows the two intersecting lines and , along with the angle between them, which is approximately .
Let me know if you'd like any further details or clarifications.
Here are some related questions to expand on this topic:
- How do you determine if two lines are parallel or perpendicular?
- What is the meaning of the slope in the context of a graph?
- How would the graph change if one of the slopes were modified?
- How can you calculate the distance between a point and a line?
- 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 .
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Math Problem Analysis
Mathematical Concepts
Analytic Geometry
Linear Equations
Angle between Lines
Formulas
Slope of a line: m = -A/B for line Ax + By + C = 0
Angle between two lines: θ = arctan |(m1 - m2) / (1 + m1*m2)|
Theorems
Slope formula
Angle between two intersecting lines
Suitable Grade Level
Grades 10-12