Don't be shy about using actual parentheses and commas.
Line through (1,8) perpendicular to
[tex] -\dfrac 4 5 x + \dfrac 5 4 y = -4[/tex]
The perpendicular family is gotten by swapping the coefficients on x and y, negating exactly one of them. The constant is given directly by the point we're through:
[tex]\dfrac 5 4 x + \dfrac 4 5 y = \dfrac 5 4 (1) + \dfrac 4 5 (8) = \dfrac 5 4 + \dfrac{32}{5}[/tex]
Let's clear the fractions by multiplying both sides by 20.
[tex] 25x + 16y = 25 + 128 = 153[/tex]
Might as well stop here.
Answer: 25 x + 16 y = 153
