Explanation:
line that is perpendicular to the given line :
y = 2/3x + 5
m1 × m2 = -1
m1 = the coefficient of x
m1 = 2/3
remember : m1 × m2 = -1
2/3 x m2 = -1
2m2 ÷ 3 = -1
(let m2 = x)
2x ÷ 3 = -1
(cross multiply)
2x = 3 × -1
2x = -3
(divide both sides by the coefficient of x)
x = -3/2
Remember : m2 =x
m2 = -3/2
The line that passes through the point (4,2) ;
( note : x¹ = 4 , y¹ = 2)
m = (y - y1) ÷ (x - x1 )
-3/2 = (y - 2) ÷ (x - 4)
(cross multiply)
-3(x - 4) = 2 (y - 2)
-3x +12 = 2y - 4
(make y the subject of formula )
-3x + 12+ 4 = 2y
-3x + 16 = 2y
(
(divide through by the coefficient of y)
-3x/ 2 + 16/2 = y
-3/2x + 8 = y
HOPE IT WAS HELPFUL