Perpendicular lines have opposite reciprocal slopes. This means that the line perpendicular to [tex]y = \frac{3x}{5} - 1 [/tex] will have a slope of -5/3. To find the new slope, inverse the given slope by flipping the fraction, and multiply by -1.
Now we can write the equation for the new line in point slope form.
y - y = m(x - x)
Replace the second y and x with the given points. Also replace m with the slope.
[tex]y - 1= \frac{-5}{3}(x+3) [/tex]
Solve for y
[tex]y = \frac{-5x}{3}- 4 [/tex]
