Answer: B. 3x+ 2y = 12
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m represents the slope of the line.
c represents the y intercept
The equation of the given line is
3x + 2y = 4
2y = -3x + 4
Dividing through by 2, it becomes
y = - 3x/2 + 2
Comparing with the slope intercept form, slope = - 3/2
If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (6, - 3) is - 3/2
To determine the y intercept, we would substitute m = - 3/2, x = 6 and y = -3 into y = mx + c. It becomes
- 3 = - 3/2 × 6 + c
- 3 = - 9 + c
c = - 3 + 9
c = 6
The equation becomes
y = -3x/2 + 6
Cross multiplying by 2, it becomes
2y = - 3x + 12
3x + 2y = 12
