Please help 100 points + brainlest
Look at the pictures below and answer them

the answers are bolded below!

Step-by-step explanation:

1. y-y1=m(x-x1)

line one- 14-4/6-1 = 10/5 = 2

so     y-1=2(x-4)

simplified     y=2x-7

line two- -2-23/1-6 = -25/5 = -5

so      y-6=-5(x-23)

simplified         y=-5x+121

b- they will intersect 1 time at (18.2,29.5)

2. No, it the system has infinitely many solutions, then the lines would be on top of each other. But since there are only two solutions, then your answer would not be infinitely many solutions.

3. y=-2x+1. This would not intersect with y=-2x+3 because they are parallel. the slopes are the same so they will each travel at the same rate but they have different y intercepts.

4. y=-2x+7 > x=-1/2y-7/2

y=-3(-1/2y+7/2)+8  > y=5

y=-2x+7 --->   5=-2x+7  > x=1

one solution at (1,5) because f graphed, the lines would only intersect once.

b- x=5

3x-y=5   --->   3(5)-y=5   --->   y=10

one solution at (5,10) because f graphed, the lines would only intersect once.

c- no solutions because if it were to be graphed, the lines would not intersect at all.

d- no solutions because if it were to be graphed, the lines would not intersect at all.

e- no solutions because if it were to be graphed, the lines would not intersect at all.

i am in algebra two so you can trust my answer. If you need more help lmk in the comments. Happy holidays and stay safe!

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!

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is