Intersection (Geometric) Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Do lines

y = 2x + 3

and

y = 2x - 5

intersect? Explain why or why not.

1
Step 1: Both lines have slope $m = 2$ . Lines with equal slopes are parallel (or identical).
2
Step 2: Their $y$ -intercepts differ ( $3 \neq -5$ ), so they are distinct parallel lines. Parallel lines in the same plane never intersect.

Answer

No intersection — the lines are parallel.

Parallel lines share the same slope but different intercepts. They never meet because they maintain a constant vertical distance (

|3 - (-5)| = 8

units) at every

x

value.

About Intersection (Geometric)

The set of all points where two or more geometric objects (lines, planes, curves) meet or cross each other.

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