Will give 50 points. no wrong what is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ? enter your answer in the box.

y= -3x+14

Step-by-step explanation:

To get the slope of the perpendicular line, get the negative reciprocal of the slope

if m=1/3, the slope of the perpendicular line is -3

Substitute the coordinates into the equation of the perpendicular line with the new slope and solve for b

2=4(-3) +b

2=-12+b

Add 12 to both sides

b=14

So, if m=-3 and b= 14 the line's equation is y= -3x+14

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!