The equation of a line is y = 2/3x + 5. What is an equation of the line that is perpendicular to the given line and that passes through the point (4, 2)?

Step-by-step 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

step-by-step explanation: