Firstly we put the equation of the line into [tex] y=mx+c [/tex] form so we can find the gradient.
[tex] -5x-4y=7 \Rightarrow -5x-7=4y \Rightarrow \frac{-5}{4}x-\frac{7}{4}=y [/tex]
So we see the gradient of the line is -5/4. The gradient of a line perpendicular to a line with gradient m is [tex] -\frac{1}{m} [/tex] so we see the gradient of a line perpendicular to your line is [tex] -\frac{1}{-\frac{5}{4}} = \frac{4}{5} [/tex].
So we know it's a line with gradient 4/5 passing through (5,2) hence
[tex] y-2=\frac{4}{5}(x-5) \Rightarrow y-2=\frac{4}{5}x-4 \Rightarrow y=\frac{4}{5}x-2 [/tex].
For the parallel line, you use the same gradient as the original which is -5/4 and using the fact that it passes through (5,2) repeat the process from above to find the line. I'll leave this one up to you!
