Write the equation of a line that is perpendicular to x=-6x=−6x, equals, minus, 6 and that passes through the point (-1,-2)(−1,−2)left parenthesis, minus, 1, comma, minus, 2, right parenthesis.

9514 1404 393

  y = -2

Step-by-step explanation:

The given line is a vertical line, so a perpendicular line will be a horizontal line. It will have an equation of the form ...

  y = constant

In order for the line to go through the given point, the constant in the equation must be the same as the y-coordinate of the point: -2.

Your perpendicular line is ...

  y = -2

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!

yes

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step-by-step explanation: