We can rewrite the equation of the given line from 3x + 4y = 12 to the slope-intercept form like this:
3x + 4y = 12
3x - 3x + 4y = 12 - 3x
4y = 12 - 3x
y = (12 - 3x)/4
y = 12/4 - 3/4x
y = 3 - (3/4)x
As you can see, the slope of this line is -3/4, since this line is parallel to the line that passes through the point (-4, 7), their slopes are the same, then we can write the equation of the second line in slope-intercept form to get:
y = -3/4x + b
By replacing the x and y-coordinates of the point (-4, 7) where the line passes through, we get:
7 = (-3/4)(-4) + b
7 = 3 + b
7 - 3 = b
4 = b
b = 4
By replacing 4 for b, into the above equation, we get: the equation of the line parallel to 3x + 4y = 12 and that passes through (-4, 7):
y = -3/4x + 4