Thank you for the opportunity to help you with your question!

15)

a) (y+4) = -2(x-3)

y + 2x -2 = 0

b) (y+4) = -0.5( x-3)

so the equation would be 2y + x + 5 = 0

16)

we assume the slope of the perpendicular to be -1/m of the given line in the equation y = mx+ c

then using the slope -1/m and using the coordinate of the given point we find the equation of the new line through the point slope form.

17) the equation is: y - 5= x

Please let me know if you need any clarification for the doubts. I'm always happy to answer your questions. Looking forward to help you again. thank you. :)