Question

The equations of three lines are given below.

Line 1: y=-3x+8
Line 2: 6x+2y=6
Line 3: y=3x+2
For each pair of fines, determine whether they are parallel, perpendicular, or neither.

Answer 1

To determine the relationships between these lines, let's analyze their slopes.

1. Line 1: y = -3x + 8

The slope of Line 1 is -3.

2. Line 2: 6x + 2y = 6

Rewrite it in slope-intercept form (y = mx + b):

2y = -6x + 6

y = -3x + 3

The slope of Line 2 is -3.

3. Line 3: y = 3x + 2

The slope of Line 3 is 3.

Now, let's compare the slopes of each pair of lines:

- Lines 1 and 2:

The slopes are both -3, which means these lines are parallel.

- Lines 1 and 3:

The slope of Line 1 is -3, and the slope of Line 3 is 3. These slopes are negative reciprocals of each other, which means these lines are perpendicular.

- Lines 2 and 3:

The slope of Line 2 is -3, and the slope of Line 3 is 3. Again, these slopes are negative reciprocals of each other, so these lines are perpendicular.

To summarize:

- Lines 1 and 2 are parallel.

- Lines 1 and 3 are perpendicular.

- Lines 2 and 3 are perpendicular.

Explanation: