Question

question 34 of 40
are the two lines parallel, perpendicular, or neither?
graph 1 image of two intersecting lines

• parallel
• perpendicular
• neither

graph 2 image of horizontal and vertical lines

• parallel
• perpendicular
• neither

graph 3 image of two vertical lines

• parallel
• perpendicular
• neither

graph 4 image of horizontal and slanted lines

• parallel
• perpendicular
• neither

Explanation:

Graph 1:

Step1: Analyze slope relationship

Parallel lines have equal slopes, perpendicular lines have slopes that are negative reciprocals (product = -1). The two lines in Graph 1 intersect at 90°? Wait, no—wait, one line has positive slope, one negative. Wait, actually, if they form a right angle, but let's check: perpendicular lines have slopes \( m_1 \) and \( m_2 \) where \( m_1 \times m_2 = -1 \). But visually, the two lines in Graph 1: one is increasing, one decreasing, and they cross at a right angle? Wait, no, maybe I missee. Wait, no—wait, Graph 1: two lines crossing. Wait, actually, if one line has slope \( m \) and the other \( -m \), but for perpendicular, product should be -1. Wait, maybe the two lines in Graph 1 are perpendicular? Wait, no, let's re-express. Wait, no—wait, the first graph: two lines intersecting. Wait, maybe I made a mistake. Wait, no, let's check each graph:

Graph 1: Two lines crossing. Let's assume their slopes: if one is \( m \) and the other is \( -1/m \), but maybe visually, they are perpendicular? Wait, no, maybe the first graph's lines are perpendicular? Wait, no, let's do each graph:

Graph 1:

Step1: Check angle

The two lines intersect at a right angle (90 degrees), so they are perpendicular.

Graph 2:

Step1: Check orientation

One line is horizontal (slope 0), one is vertical (undefined slope). Horizontal and vertical lines are perpendicular (since 0 and undefined slope, and they form 90° angle).

Graph 3:

Step1: Check slope

Both lines are vertical (same undefined slope), so they are parallel.

Graph 4:

Step1: Check slope

One line is horizontal (slope 0), one has a positive slope (not 0, not undefined). So they are neither parallel (different slopes) nor perpendicular (product of slopes: 0 × m = 0 ≠ -1).

Answer:

s:
Graph 1: Perpendicular
Graph 2: Perpendicular
Graph 3: Parallel
Graph 4: Neither