Let's begin by listing out the information given to us:
[tex]\begin{gathered} 25x+15y=9----1 \\ 5y=3x-10-----2 \end{gathered}[/tex]To know this, we will calculate the slope:
[tex]\begin{gathered} y=mx+b \\ where\colon m=slope \\ 25x+15y=9 \\ We\text{ will make variable y the subject of the formula},\text{ subtract 25x from both sides} \\ 25x-25x+15y=-25x+9 \\ 15y=-25x+9 \\ \text{divide through by 15 (the coefficient of y)} \\ \frac{15y}{15}=-\frac{25}{15}x+\frac{9}{15} \\ y=-\frac{5}{3}x+\frac{3}{5};m=-\frac{5}{3} \\ \\ 5y=3x-10 \\ \text{divide through by 5 (the coefficient of y)} \\ \frac{5y}{5}=\frac{3}{5}x-\frac{10}{5} \\ y=\frac{3}{5}x-2;m=\frac{3}{5} \end{gathered}[/tex]We will see that the slopes of the two equations are a negative reciprocal (-1/m) of one another. This therefore informs us that the lines are parallel to one another
