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:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.