The definition of a parallel line is one that has the same slope.

In the equation Y = mx+b, m is the slope, and thus must remain constant to find a parallel line. So the first step is to find the slope of the line of the equation given. Do this by solving for Y.

4x = 5y + 7, 5y = 4x - 7, y = (4/5)x - 7/5

From this equation, we can see that the slope of the line is 4/5. This means the equation for the parallel line will have the form: y = (4/5)x + b

All that's left is to solve for b, using the point given.

4 = (4/5)*-2 + b

b = 4 + 2*4/5 = 4 + 8/5 = 5 3/5

Sub this into our equation and you get the final answer:

Y = (4/5)x + 5 3/5

In the equation Y = mx+b, m is the slope, and thus must remain constant to find a parallel line. So the first step is to find the slope of the line of the equation given. Do this by solving for Y.

4x = 5y + 7, 5y = 4x - 7, y = (4/5)x - 7/5

From this equation, we can see that the slope of the line is 4/5. This means the equation for the parallel line will have the form: y = (4/5)x + b

All that's left is to solve for b, using the point given.

4 = (4/5)*-2 + b

b = 4 + 2*4/5 = 4 + 8/5 = 5 3/5

Sub this into our equation and you get the final answer:

Y = (4/5)x + 5 3/5