Answer:
Option B (3x - 4y = -4).
Explanation:
Parallel lines are the straight lines that never meet. This is only possible when the gradients of both the lines are same. This means that the slopes of all the parallel lines in a group can be calculated by calculating the slope of one of the lines. Therefore, the slope of the line that is parallel to the line 3x-4y=7 is the same as the original line. Hence, the gradient can be extracted from the original line by converting the equation in the form y=mx+c, where m is the slope.
3x - 7 = 4y.
y = (3/4)x - 7/4.
The slope of the line which has to be found is 3/4 and it passes through (x0, y0) = (-4, -2). Using the following formula:
(y - y0) = m*(x - x0).
(y + 2) = (3/4)*(x + 4)
Cross multiplying:
4y + 8 = 3x + 12.
3x - 4y = -4.
Hence, Option B is the correct choice!!!