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