Question 290658
First convert both equations to slope intercept form which is 
y = mx + b  with m being the slope and b is the y intercept

Equation 1:
4x-3y=-9  subtract 4x from both sides
-3y = -4x - 9  divide both sides by -3
y = (4/3)x + 3  so the slope in equation 1 is 4/3

Equation 2:
7x + 4y = 7   subtract 7x from both sides
4y = -7x + 7  divide both sides by 4
y = (-7/4)x + 7/4 so the y-intercept is 7/4

Now parallel lines have the same slope.

the problem wants us to find the equation using the slope from equation 1 and the y intercept from equation 2

therefore the new equation will be:  using the form y = mx + b
So:  y = (4/3)x + 7/4