Two parallel lines have the same slope.
[tex]\begin{gathered} y=mx+b \\ m=\text{slope} \end{gathered}[/tex]
In the given equation the slope is:
[tex]\begin{gathered} y=\frac{8}{5}x-1 \\ \\ m=\frac{8}{5} \end{gathered}[/tex]
Then, you need to write the equations to slope-intercept form (solve for y) to identiy the slope:
Option 1
[tex]\begin{gathered} 8x+5y=35 \\ 5y=-8x+35 \\ y=-\frac{8}{5}x+\frac{35}{5} \\ \\ y=-\frac{8}{5}x+7 \end{gathered}[/tex]
The slope in this one is -8/5. (Is not parallel to the given equation)
Option 2:
[tex]\begin{gathered} 5x+8y=-24 \\ 8y=-5x-24 \\ y=-\frac{5}{8}x-\frac{24}{8} \\ \\ y=-\frac{5}{8}x-3 \end{gathered}[/tex]
The slope in this one is -5/8. (Is not parallel to the given equation)
Option 3:
[tex]\begin{gathered} 5x-8y=-32 \\ -8y=-5x-32 \\ y=\frac{-5}{-8}x-\frac{32}{-8} \\ \\ y=\frac{5}{8}x+4 \end{gathered}[/tex]
The slope in this one is 5/8. (Is not parallel to the given equation)
Option 4:
[tex]\begin{gathered} 5y-8x=-35 \\ 5y=8x-35 \\ y=\frac{8}{5}x-\frac{35}{5} \\ \\ y=\frac{8}{5}x-7 \end{gathered}[/tex]
The slope in this one is 8/5. This line is parallel to the given equation.
Answer: Option 4 (5y-8x=-35)
