Question

The coordinate plane below represents a community. Points A through F are houses in the community.

graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.

Part A: Using the graph above, create a system of inequalities that only contains points B and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

Part B: Explain how to verify that the points B and F are solutions to the system of inequalities created in Part A. (3 points)

Part C: John wants to live in the area defined by y > 2x − 5. Explain how you can identify the houses in which John is interested in living. (2 points)

Answer 1

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Answer 2

also i think i have part A so if someone could check that be lit

Answer 3

@Vocaloid

Answer 4

ok, so what inequalities did you get for part A?

Answer 5

y<x and y>-2x

Answer 6

ok, let me just check that by plotting the lines

Answer 7

hm. the shaded region contains C+F not B+F so we will have to try some different inequalities.

Answer 8

OH yeah

Answer 9

hm

Answer 10

below the reddish line and above the blue line should work i think, can you try writing the inequalities?

Answer 11

hold on gimme a sec let me see

Answer 12

Ugh i just can't figure it out

Answer 13

since we have a graph we can use the rise/run method to find the slope

Answer 14

2 units across, 1 unit down

so rise/run = (-1)/2 = -1/2 as the slope

the red line passes through the origin so

y = mx + b = (-1/2)x + 0, or in other words

y = (-1/2)x for the red line

Answer 15

for that second line, it goes 1 unit across and 1 unit down

so rise/run = 1/(-1) = -1, making the slope -1

it's not clear from the graph but if we extend that line it crosses the y-axis at -8 making the y-intercept -8

so the equation becomes y = -x - 8

Answer 16

now, we said that the shaded region is below the red line and above the blue line

we modify the equations to get

y < -(1/2)x
and
y > -x - 8

as the set of inequalities for part A

Answer 17

for part B, it says to explain how one might verify that B and F are solutions to the inequality

you could just say something like, "plug in the values of x and y for points B and F and check that they satisfy the inequality" [not sure if they want the calculations or not]

Answer 18

Ohhhhh

Answer 19

and for part C you would just graph y > 2x - 5 on the same graph, shade, and see which houses fall within the shaded region

Answer 20

oh okay so for part c i would see which ones like a,b, all them and there points are within the shaded region of just that inequality given right?

Answer 21

yeah, just the inequality y > 2x - 5

Answer 22

alright thank you so much!