Math Problem Statement

True or false? Parallel lines have the same slope, so a system consisting of 2 parallel lines will cross at one specific point.

Solution

The statement is false.

Parallel lines have the same slope but different y-intercepts, which means they never intersect. A system of two parallel lines will have no points of intersection, as they are always the same distance apart. Therefore, they do not cross at any point.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the geometric definition of parallel lines?
  2. How can we determine if two lines are parallel given their equations?
  3. What happens when two lines in a system have the same slope and y-intercept?
  4. Can two lines with different slopes ever be parallel?
  5. How do perpendicular lines differ from parallel lines?

Tip: If the slopes of two lines are equal but their y-intercepts are different, they are parallel and will never meet.

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Math Problem Analysis

Mathematical Concepts

Geometry
Linear Equations
Parallel Lines
Slope

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Parallel Line Theorem: Parallel lines have the same slope but different y-intercepts

Suitable Grade Level

Grades 8-10