What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=5/4 x-2?

Hey there :)

[tex]y = \frac{5}{4}x - 2 [/tex]
Slope is the coefficient of x ⇒ [tex] \frac{5}{4} [/tex]

If the second line is perpendicular to the given line, then the slope of the 2nd line is the reverse/reciprocal of the 1st line ⇒ [tex] \frac{4}{5} [/tex]

(10, 5)
  ↑  ↑
  x₁ y₁

Point-slope form is ( y - y₁ ) = m ( x - x₁ )

y - 4 = [tex] \frac{4}{5} [/tex] ( x - 10 )
y - 4 = [tex] \frac{4}{5} x[/tex] - 8

y = [tex] \frac{4}{5} x - 4[/tex] ⇔ The equation of the line that passes through the point (10,5) ans perpendicular to the given line