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 x+y+1=0x + y + 1 = 0 and 2xy1=02x - y - 1 = 0, along with the angle between them, which is approximately 71.5771.57^\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 1-1.

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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