Question

geometry, measurement, data analysis
identifying parallel and perpendicular lines
for each graph, decide if the two lines are parallel, perpendicular, or neither.
graph 1
image of two horizontal lines
options: parallel, perpendicular, neither
graph 2
image of horizontal and vertical lines (cross)
options: parallel, perpendicular, neither
graph 3
image of two lines (one slightly slanted?)
options: parallel, perpendicular, neither
graph 4
image of two intersecting lines
options: parallel, perpendicular, neither

Explanation:

Graph 1

Step1: Recall parallel lines definition

Parallel lines never intersect and have same slope.

Step2: Analyze Graph 1 lines

The two lines are horizontal, same direction, no intersection. So they are parallel.

Graph 2

Step1: Recall perpendicular lines definition

Perpendicular lines intersect at 90° (right angle), slopes are negative reciprocals.

Step2: Analyze Graph 2 lines

One horizontal, one vertical, intersect at right angle. So they are perpendicular.

Graph 3

Step1: Recall parallel/perpendicular definitions

Parallel: same slope, no intersection. Perpendicular: 90° intersection.

Step2: Analyze Graph 3 lines

Lines have different slopes (not parallel) and don't intersect at 90° (not perpendicular). So neither.

Graph 4

Answer:

Graph 1: Parallel
Graph 2: Perpendicular
Graph 3: Neither
Graph 4: Perpendicular (Wait, no—wait, maybe Graph 4: if the two lines cross and form a right angle, then perpendicular. Wait, maybe I was wrong earlier. Let's confirm:

• Parallel lines: same direction, never meet.
• Perpendicular: meet at 90 degrees.

Graph 1: two horizontal lines—parallel.
Graph 2: horizontal and vertical—perpendicular.
Graph 3: two lines with different slopes, not parallel, not 90°—neither.
Graph 4: two lines intersecting at 90°? Wait, maybe the lines are perpendicular. Wait, maybe the answer is:

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

Wait, but maybe Graph 4 is neither? Wait, no—let's check the slopes. If one line has slope 1 (rising) and the other -1 (falling), they are perpendicular. So yes, perpendicular. So final answers:

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