Question 548266
Let's look at the first part:
Determine the equation of the line which is parallel to the line 4x - 5y = 9

We know that parallel lines have the same slope (m value) 
We can rearrange this formula into y=mx+b and find that m-value.  

{{{4x-5y=9}}}
{{{4x-5y+5y-9=9+5y-9}}} 
{{{4x-9=5y}}} 
{{{(4x-9)/5=5y/5}}} 
{{{(4x-9)/5=y}}} 
{{{y=(4/5)*x-9/5}}} 
So the m value is 4/5 


For the second part, 
Again we can rearrange (2x) / 3 + (4y) / 5 = 8  into y=mx+b form and the b value will be the y-intercept 


{{{(2x) / 3 + (4y) / 5 = 8}}}
Multiple every term by 3
{{{3*((2x) / 3) + 3*((4y) / 5) = 3*8}}}
{{{(2x) + ((12y) / 5) = 24}}}

Now multiply every term by 5
{{{5*(2x) + 5*((12y) / 5) = 5*24}}}
{{{(10x) + (12y) = 120}}}
{{{(10x) + (12y) -10x= 120-10x}}}
{{{12y= 120-10x}}}
{{{12y/12= 120/12-10x/12}}}
{{{y= 10-10/12*x}}}
{{{y=-10/12*x+10}}}
From this we see that the b-value is 10




Since the line we are looking for has the same slope and same y-intercept, we can plug these values right into the y-intercept form of a line (y=mx+b).  This leaves:
{{{y=4/5*x+10}}}


Hopefully this helps:)