For this case, we have that by definition, two lines of the form y = f (x) are parallel if they have the same slope, that is:
![m_ {1} = m_ {2}](https://img.qammunity.org/2020/formulas/mathematics/college/gagott3nrl9huqoecneuxh6h8ss2ymeypg.png)
In this case we have the following line:
![y = \frac {3} {4} x + \frac {2} {5}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6t50zvx0wssg754nw6ld65j4gkyi3qm88h.png)
Your slope is:
![m_ {1} = \frac {3} {4}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/avv7bn2kbs3xgusrqaise6velmclaqlfkc.png)
Then, a parallel line must have slope:
![m_ {2} = \frac {3} {4}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/1o6lpy1je870cwp8khd49lxlqaa126zo1m.png)
Then, the correct option is:
![f (x) = \frac {3} {4} x + 9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/sdi53z4koehuk55jnd64c0ktuq4za90b7x.png)
Answer:
Option A