Question

The equations of three lines are given below.

line 1: 3y = -4x + 4
line 2: 6x + 8y = 6
line 3: y = - 4 / 3 x - 7
the fraction is negative
for each pair of lines, determine whether they are parallel, perpendicular, or neither.
line 1 and line 2: parallel, perpendicular, or neither
line 1 and line 3: parallel, perpendicular, or neither
line 2 and line 3: parallel, perpendicular, or neither

Answer 1

Two lines are parallel if their slopes are equal. Two lines are perpendicular if their slopes are negative reciprocals.

Step-by-step explanation:

When determining whether two lines are parallel or perpendicular, we can look at their slopes.

For line 1 and line 2:

• Line 1 has a slope of -4/3.
• Line 2 has a slope of -3/4.

Since the slopes are neither equal nor negative reciprocals, line 1 and line 2 are neither parallel nor perpendicular to each other.

For line 1 and line 3:

• Line 1 has a slope of -4/3.
• Line 3 has a slope of -4/3.

Since the slopes are equal, line 1 and line 3 are parallel to each other.

For line 2 and line 3:

• Line 2 has a slope of -3/4.
• Line 3 has a slope of -4/3.

Since the slopes are negative reciprocals, line 2 and line 3 are perpendicular to each other.