Two lines are perpendicular if the product of their slopes is -1. In this example, the slope of one of the slopes is -5/3 (the coefficient of the x variable when the equation is solved for y), then the slope of the new line must satisfy
![\begin{gathered} -(5)/(3)m=-1 \\ m=(3)/(5) \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/sfujwt4aj6ko0nltn33w.png)
Using the point-slope form, we have
![\begin{gathered} y-(-1)=(3)/(5)(x-(-5)) \\ y+1=(3)/(5)x+3 \\ y=(3)/(5)x+2 \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/wb3fkz33hxs91tvgd6dz.png)
Then, the slope-intercept form of the equation is
![y=(3)/(5)x+2](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/5166hd9ovkadx9f2px1c.png)