Question

The coordinate plane below represents a city. Points A through F are schools in the city.

Answer 1

Using the graph above, create a system of inequalities that only contain points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A.

Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x - 3. Explain how you can identify the schools that Timothy is allowed to attend.

Answer 2

@Preetha

Answer 3

@phi

Answer 4

I've been on this forever now :(

Answer 5

I would draw 2 lines. one horizontal and one vertical to "isolate" points D and E
can you do that ? (just draw them, forget about the math for the moment)

Answer 6

Okay, One minute

Answer 7

I already did this problem... can you follow the instructions for that post?

Answer 8

will this work? or do i need to move the vertical line a bit, because i think it should be intersecting D

Answer 9

the lines does not have to go through the points.
we need to say the points are above or below one line
and to the left or right of the other.

Answer 10

do you know how to write the equation of a horizontal line? specifically, the one you drew?

Answer 11

would this be better?

Answer 12

the first would have worked. this one also works.

But the next question is, "what is the equation of the horizontal line"
any idea?

Answer 13

yes, its y = 3

Answer 14

and the vertical is x =-3

Answer 15

for the horizontal line you can use
y = mx +b
and figure out its slope=0 and b= 3 to get y=3

Answer 16

ok we have the 2 lines.
next step. which side of the horizontal line are points D and E? i.e. above or below.
clearly above.
above means *bigger* y values than the y value of the line.

Answer 17

so do we use an inequality?

Answer 18

do you know how to write all y's bigger than 3 ?

Answer 19

y > 3

Answer 20

yes. btw, for your first try (where the line went through points D and E would we have used y >= 3 )

but now to the other line, x=-3
we want the the right side of x=-3, which means all x's bigger than -3
how do you write that inequality?

Answer 21

x > -3

Answer 22

and that is your system of equations
x>-3
y>3

you would graph the *lines* y=3 and x= -3 but use "dashes" (because it is > in both cases)
and then shade in the area above y=3 and to the right of x=-3

Answer 23

ok on that ?

Answer 24

yes, thank you, is that it for part A?

Answer 25

now for
*** Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A.
***

to verify point D (or E) is in that region, take the (x,y) values and use them in each inequality
x>-3
y>3

if both inequalities are true for the point, then that point is a solution for the system.

Answer 26

Example: D is (-2,4)
x value of D is -2, y value is 4
test in x>-3 , -2 > -3 ? YES
test in y > 3, 4 > 3 ? YES
so D is a solution.

do the same for point E

Answer 27

E = (2, 4)

x = 2
y = 4

x > -3 2 > -3
y > 3 4 > 3

Answer 28

@phi

Answer 29

Is that it for part B?

Answer 30

Graph the line y < 3x - 3 on a coordinate plane. Graph the number 3 on the y-axis and use the slope of 3, to graph the line. Go up 3, right 1, 3/1. Repeat this until you have enough points. Connect the points on the graph and shade to the right. The line is dashed.

Timothy can only attend either school C, or F.

Answer 31

yes, just mention that point E works for both inequalities.

Answer 32

that's my answer for part C

Answer 33

ok for part C except you only need 2 points (and a ruler so you draw a straight line)
and y < 3x -3 could also be interpreted as "below" the dashed line y= 3x-3

Answer 34

Okay, thank you so much! :)

Answer 35

yw