SOLUTION: I need Help!!!!!! Find a linear inequality with the following solution set. Each grid line represents one unit. Graph: https://latex.artofproblemsolving.com/4/8/2/48234b947b6

Algebra ->  Graphs -> SOLUTION: I need Help!!!!!! Find a linear inequality with the following solution set. Each grid line represents one unit. Graph: https://latex.artofproblemsolving.com/4/8/2/48234b947b6      Log On


   

Question 1154175: I need Help!!!!!!
Find a linear inequality with the following solution set. Each grid line represents one unit.
Graph: https://latex.artofproblemsolving.com/4/8/2/48234b947b623e95b3f920ee2e9ce6cb24dcfa4b.png
Give your answer in the form $ax+by+c>0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater than 1
Thanks!!!!
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The dotted line between the two regions means that this line is excluded from the solution region.

Two points which can be observed on the boundary line are (3,1) and (-3,-2).
This boundary line's equation: y-1=%28%281-%28-2%29%29%2F%283-%28-3%29%29%29%28x-3%29
y-1=%281%2F2%29%28x-3%29
2%28y-1%29=x-3
2y-2=x-3
0=x-2y-3%2B2
x-2y-1=0------------just the boundary line equation.

If you want the yellow, upper region to be the solution then x-2y-1%3C0.
If you want the darkened, lower region to be the solution then x-2y-1%3E0.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The y-intercept of the boundary line is -0.5; the slope is 0.5. The equation of the boundary line in slope-intercept form is

y+=+0.5x-0.5

The solution set is ABOVE the boundary line; the inequality is

y+%3E+0.5x-0.5

The problem asks for the answer in ax+by+c>0 form:

y+%3E+0.5x-0.5
2y+%3E+x-1
2y-x%2B1+%3E+0
-x%2B2y%2B1+%3E+0

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

The required inequality is


    y > %281%2F2%29x-1%2F2       (1)


Tthe solution set is the set of all points (x,y) of the coordinate plane ABOVE the straight line 
(the domain shown YELLOW in the plot)


    y = %281%2F2%29x+-+1%2F2.    (2)


The straight line itself is not included into the solution set.


Inequality (1) can be EQUIVALENTLY presented in the form


    2y - x + 1 > 0,            (3)


which has the required form.

Solved, answered, explained and completed.