Answer:
The equation is 5x - 4y = 76
Step-by-step explanation:
∵ The equation of the line 5y = -4x⇒ divide each side by 5
∴ y = -4/5 x ⇒ the slope of this line = [tex]\frac{-4}{5}[/tex]
∵ The two lines are ⊥
∴ The product of their slopes = -1
∴ The slope of the ⊥ line is [tex]\frac{5}{4}[/tex] (additive and multiplicative inverse of the first slope)
∵ (y - y1) = m (x - x1) ⇒ m is the slope and (x1 , y1) point on the line
∴ y - (-4) = 5/4 (x - 12)
∴ y + 4 = 5/4 x - 15 ⇒ multiply both side by 4
∴ 4y + 16 = 5x - 60 ⇒ collect like terms
∴ 5x - 4y = 76
∴ The equation of the ⊥ line in standard form is 5x - 4y = 76
