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To find the equation of a line parallel to 3x - 2y = -12, we first need to determine the slope of the given line.
1. Convert the given equation to slope-intercept form (y = mx + b), where m is the slope:
3x - 2y = -12
-2y = -3x - 12
y = 3/2x + 6
2. Since the line we are looking for is parallel to this line, it will have the same slope (3/2).
3. Use the point-slope form of a linear equation to find the equation of the line passing through the point (-2,4) with the slope of 3/2:
y - y₁ = m(x - x₁)
y - 4 = 3/2(x + 2)
y - 4 = 3/2x + 3
y = 3/2x + 7
Therefore, the equation of the line parallel to 3x - 2y = -12 that passes through the point (-2,4) is:
Oy = 3/2x + 7
Among the answer choices provided, the correct answer is:
Oy = 3/2x + 7
I hope this explanation helps! Let me know if you have any more questions.
