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

- anonymous

- schrodinger

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- anonymous

##### 1 Attachment

- Vocaloid

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

- anonymous

y=1/ 1/2+3

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## More answers

- anonymous

?

- Vocaloid

uh... not quite

- Vocaloid

|dw:1443914795869:dw|
lets focus on one line at a time. what is the equation of this line?

- anonymous

ok

- Vocaloid

|dw:1443914881362:dw|
write the equation for this line please

- anonymous

y=3x-3 ? @Vocaloid

- Vocaloid

nope
first find the slope of the graph

- Vocaloid

(x1,y1) = (-3,0)
(x2,y2) = (0,3)
slope = m = (y2-y1)/(x2-x1) = ?

- anonymous

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

- Vocaloid

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

- anonymous

-3 and -3

- Vocaloid

keep going

- Vocaloid

/ means divide...

- Vocaloid

-3/-3 = ?

- anonymous

1

- anonymous

- Vocaloid

good, so our slope is 1
now find the y-intercept

- anonymous

- Vocaloid

good, so our equation is y = x + 3
now write an equation for the other line

- anonymous

0,3 and -1, 2?

- anonymous

- Vocaloid

uh not quite

- Vocaloid

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

- Vocaloid

|dw:1443916158259:dw|

- anonymous

ill i can see is 3/ 1.5

- anonymous

- Vocaloid

not quite...

- Vocaloid

two points are
(0,3)
and
(2,-1)
now calculate the slope between them

- anonymous

-1

- anonymous

- texaschic101

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

- texaschic101

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

- mathstudent55

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."

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