anonymous
  • anonymous
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
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
1 Attachment
Vocaloid
  • 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
  • anonymous
y=1/ 1/2+3

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anonymous
  • anonymous
?
Vocaloid
  • Vocaloid
uh... not quite
Vocaloid
  • Vocaloid
|dw:1443914795869:dw| lets focus on one line at a time. what is the equation of this line?
anonymous
  • anonymous
ok
Vocaloid
  • Vocaloid
|dw:1443914881362:dw| write the equation for this line please
anonymous
  • anonymous
y=3x-3 ? @Vocaloid
Vocaloid
  • Vocaloid
nope first find the slope of the graph
Vocaloid
  • Vocaloid
(x1,y1) = (-3,0) (x2,y2) = (0,3) slope = m = (y2-y1)/(x2-x1) = ?
anonymous
  • anonymous
(0-3) and -3-0 @Vocaloid
Vocaloid
  • Vocaloid
keep going (0-3)/(-3-0) = ?
anonymous
  • anonymous
-3 and -3
Vocaloid
  • Vocaloid
keep going
Vocaloid
  • Vocaloid
/ means divide...
Vocaloid
  • Vocaloid
-3/-3 = ?
anonymous
  • anonymous
1
anonymous
  • anonymous
Vocaloid
  • Vocaloid
good, so our slope is 1 now find the y-intercept
anonymous
  • anonymous
Vocaloid
  • Vocaloid
good, so our equation is y = x + 3 now write an equation for the other line
anonymous
  • anonymous
0,3 and -1, 2?
anonymous
  • anonymous
Vocaloid
  • Vocaloid
uh not quite
Vocaloid
  • Vocaloid
look at the graph and pick two points on the line on the right
Vocaloid
  • Vocaloid
|dw:1443916158259:dw|
anonymous
  • anonymous
ill i can see is 3/ 1.5
anonymous
  • anonymous
Vocaloid
  • Vocaloid
not quite...
Vocaloid
  • Vocaloid
two points are (0,3) and (2,-1) now calculate the slope between them
anonymous
  • anonymous
-1
anonymous
  • anonymous
texaschic101
  • 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
  • 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
  • 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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