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The equations of three lines are given below.Line 1: 4x - 6y = 2Line 2: y = 3/2 * x - 7Line 3: 2y = 3x + 5For each pair of lines, determine whether they are parallel, perpendicular, or neither.

The equations of three lines are given below.Line 1: 4x - 6y = 2Line 2: y = 3/2 * x-example-1

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Answer:

Step-by-step explanation:

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

Considering equation 1,

4x - 6y = 2

By rearranging the equation,

4x - 2 = 6y

6y = 4x - 2

Dividing both sides of the equation by 6, we have

6y/6 = 4x/6 - 2/6

y = 2x/3 - 1/3

Thus, slope = 2/3

Considering equation 2,

y = 3x/2 - 7

slope = 3/2

Considering equation 3,

2y = 3x + 5

Dividing both sides by 2,

2y/2 = 3x/2 + 5/2

y = 3x/2 + 5/2

slope = 3/2

Recall, two lines are parallel if they have equal slope. the slopes of equation 2 and 3 is 3/2. Since it is equal,

Line 1 and line 2 : neither

Line 1 and Line 3: neither

line 2 and line 3 are parallel