Which point lies on the line with point-slope equation y - 3 = 4(x + 7)? A.
(7, 3)

B.
(7, -3)

C.
(-7, -3)

D.
(-7, 3)

Step-by-step explanation:

The standard form of a point slope equation of a line is expressed as shown;

y-y₀ = m(x-x₀) where;

m is the slope of the line

(x₀, y₀) is the coordinate of the point that lies in the line.

Comparing the standard equation given with the equation in question

y - 3 = 4(x + 7) to get the point on the line we will have;

y₀  = 3 and -x₀ = 7

for -x₀ = 7;

multiply both sides with a minus sign

-(-x₀) = -7

x₀ = -7

Hence the coordinate of the point required (x₀, y₀) is (-7, 3).

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!

associative property hopes this ! : )

step-by-step explanation: