We have the next equation line:
![3x-y\text{ = 5}](https://img.qammunity.org/2023/formulas/mathematics/college/8ytw75au66rlpf4fq7m567t4n3boq7ykut.png)
We need to solve the equation for y to get the equation form
![-y\text{ =5-3x}](https://img.qammunity.org/2023/formulas/mathematics/college/lh9mzy00i5tt1tf6mhwyolx64dpzcnlxig.png)
Multiply the equation by -1
![(-1)-y\text{ =(-1)(5-3x)}](https://img.qammunity.org/2023/formulas/mathematics/college/jfnxihny7h94y8rwpy17xc7tccm1qa6274.png)
![y\text{ = -5+3x}](https://img.qammunity.org/2023/formulas/mathematics/college/23a2yqlozr4pi6eywk913v1k1f43e5d852.png)
Where the y-intercept is -5 and the slope is 3x.
To find the line parallel we need to know that the parallel lines have the same slope.
The parallel line also intercepts y at point (0,-7).
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
Replace the slope=m = 3
and the y-intercept is -7.
So the parallel line is:
![y=3x-7](https://img.qammunity.org/2023/formulas/mathematics/high-school/rst1k3yatqhc061ap04y1pra3jcv19hiae.png)