A characteristic of parallel lines is that they have the same slope.
So for the line
[tex]y=\frac{5}{4}x-7[/tex]The slope is
[tex]m=\frac{5}{4}[/tex]Any line parallel to this one will have the same slope:
[tex]y=\frac{5}{4}x+b[/tex]Foe example, let's say that the parallel line has to pass through the point (2,3)
Using the point slope form you can determine the equation as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{5}{4}(x-2) \\ y-3=\frac{5}{4}x-\frac{5}{2} \\ y=\frac{5}{4}x-\frac{5}{2}+3 \\ y=\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]The line
[tex]y=\frac{5}{4}x+\frac{1}{2}[/tex]is parallel to
[tex]y=\frac{5}{4}x-7[/tex]