Question

The graph below represents which system of inequalities?


y less than or greater to -2x + 3
y less than or greater to x + 3
y greater than or equal to -2x + 3
y greater than or equal to x + 3
y less than or greater to -3x + 2
y less than or greater to -x + 2
y > -2x + 3
y > x + 3

Answer 1

hint: ignore the green and yellow for now, just focus on the two black lines

write the equations for the lines in point intercept form

Answer 2

y=1/ 1/2+3

Answer 3

?

Answer 4

uh... not quite

Answer 5

lets focus on one line at a time. what is the equation of this line?

Answer 6

ok

Answer 7

write the equation for this line please

Answer 8

y=3x-3 ? @Vocaloid

Answer 9

nope

first find the slope of the graph

Answer 10

(x1,y1) = (-3,0)
(x2,y2) = (0,3)

slope = m = (y2-y1)/(x2-x1) = ?

Answer 11

(0-3) and -3-0 @Vocaloid

Answer 12

keep going

(0-3)/(-3-0) = ?

Answer 13

-3 and -3

Answer 14

keep going

Answer 15

/ means divide...

Answer 16

-3/-3 = ?

Answer 17

1

Answer 18

@Vocaloid

Answer 19

good, so our slope is 1

now find the y-intercept

Answer 20

3 @Vocaloid

Answer 21

good, so our equation is y = x + 3

now write an equation for the other line

Answer 22

0,3 and -1, 2?

Answer 23

@Vocaloid

Answer 24

uh not quite

Answer 25

look at the graph and pick two points on the line on the right

Answer 26

ill i can see is 3/ 1.5

Answer 27

@Vocaloid

Answer 28

not quite...

Answer 29

two points are

(0,3)
and
(2,-1)

now calculate the slope between them

Answer 30

-1

Answer 31

@Vocaloid

Answer 32

slope = (y2 - y1) / (x2 - x1)
(0,3)....x1 = 0 and y1 = 3
(2,-1)....x2 = 2 and y2 = -1

now we sub
slope(m) = (-1 - 3) / (2 - 0)
slope(m) = -4/2
slope(m) = -2

now we use y = mx + b
slope(m) = -2
use either of your sets of points....(0,3)...x = 0 and y = 3
now we sub into the formula to solve for b, the y intercept
3 = -2(0) + b
3 = b

so the equation for that line is : y = -2x + 3

Answer 33

now take your 2 lines...
y = x + 3 and y = -2x + 3

notice that both lines are solid...this means they both contain equal signs.
notice that both lines are shaded below the line....this means that both lines are less then <.

so the inequalities that match the graph are :
y <= x + 3 and y <= 2x + 3

Answer 34

This is how you solve this quickly since we are given choices.

1. Both lines are solid; that means either >= or <=, but not > or <.

2. Both lines have the shaded area under the solid line. That means y <= ax + b.

3. Both lines have y-intercepts of 3. That means both inequalities are of the form
y <= ax + 3

The only set of inequalities that satisfies all conditions above is choice A.

Of course, this is assuming that where you wrote "less than or greater to" you really meant "less than or equal to."