Question

for each graph, decide if the two lines are parallel, perpendicular, or neither. graph 1 graph 2 graph 3 graph 4 four graphs (each with two lines) shown below the labels for each graph, options: parallel, perpendicular, neither (repeated for graph 1, graph 2, graph 3, graph 4)

Explanation:

To solve this, we analyze each graph based on the definitions of parallel and perpendicular lines:

Graph 1

• Parallel lines never intersect and have the same slope. The two horizontal lines here are parallel (they run side - by - side, same direction, no intersection).

So for Graph 1, the answer is Parallel.

Graph 2

• Parallel lines have the same slope, perpendicular lines have slopes that are negative reciprocals (product = - 1). The two lines here have different slopes (one is a slanted line, one is a vertical - like line) and don't intersect at 90 degrees.

So for Graph 2, the answer is Neither.

Graph 3

• Perpendicular lines intersect at a 90 - degree angle. The two lines (one horizontal, one vertical) intersect at right angles.

So for Graph 3, the answer is Perpendicular.

Graph 4

• The two lines meet at a point but not at a 90 - degree angle, and they are not parallel (they converge).

So for Graph 4, the answer is Neither.

Final Answers:

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

Answer:

To solve this, we analyze each graph based on the definitions of parallel and perpendicular lines:

Graph 1

• Parallel lines never intersect and have the same slope. The two horizontal lines here are parallel (they run side - by - side, same direction, no intersection).

So for Graph 1, the answer is Parallel.

Graph 2

• Parallel lines have the same slope, perpendicular lines have slopes that are negative reciprocals (product = - 1). The two lines here have different slopes (one is a slanted line, one is a vertical - like line) and don't intersect at 90 degrees.

So for Graph 2, the answer is Neither.

Graph 3

• Perpendicular lines intersect at a 90 - degree angle. The two lines (one horizontal, one vertical) intersect at right angles.

So for Graph 3, the answer is Perpendicular.

Graph 4

• The two lines meet at a point but not at a 90 - degree angle, and they are not parallel (they converge).

So for Graph 4, the answer is Neither.

Final Answers:

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