Math Problem Statement
Solution
The image shows two lines graphed on a coordinate plane, and you are asked to determine whether the lines are parallel, perpendicular, or neither.
Analysis:
- Parallel lines have the same slope and never intersect.
- Perpendicular lines have slopes that are negative reciprocals of each other (i.e., the product of their slopes is -1).
- Neither means the lines are neither parallel nor perpendicular, but they intersect.
Observing the graph:
- The two lines clearly intersect at a point that is not a right angle.
- Since they are not perpendicular (no right angle) and their slopes differ, they are neither parallel nor perpendicular.
Thus, the correct answer is:
- Neither.
Would you like more details on how to calculate slopes, or do you have any other questions?
Here are 5 related questions:
- How do you calculate the slope of a line from a graph?
- What conditions must two lines satisfy to be perpendicular?
- Can two lines be perpendicular if they intersect at any angle other than 90 degrees?
- How can you determine if two lines are parallel algebraically?
- Why is the concept of slope important in geometry?
Tip: To quickly check if two lines are perpendicular, find their slopes. If the product of the slopes equals -1, they are perpendicular!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Coordinate Geometry
Formulas
Slope formula: (y2 - y1) / (x2 - x1)
Condition for parallelism: slopes are equal
Condition for perpendicularity: product of slopes equals -1
Theorems
Slope-intercept form y = mx + b
Parallel and Perpendicular Line Theorem
Suitable Grade Level
Grades 7-10
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