Find a linear inequality with the following solution set. Each grid line represents one unit.
https://latex.artofproblemsolving.com/4/8/2/48234b947b623e95b3f920ee2e9ce6cb24dcfa4b.png - Link to graph
(Give your answer in the form $ax+by+c>0$ or $ax+by+c\geq0$ where a and b are integers with no common factor greater than 1.)
Incorrect answers -
y > 1/2x - 1/2
y+x<=1
3x - 2y < 7
x+y-1>0
2x - 3y + 1 > 0
(3x - 7) / 2 > 0
+36916 Shaded area is everything above the line but not including the line
line equation is y = 1/2x - 1/2
answer y > 1/2x - 1/2 <======== you have this listed as incorrect answer....but it IS correct ! You just need to complet the work to get it in the correct form....don't be a lazy person just looking for the answer !
y > 1/2x - 1/2
0 > 1/2x - 1/2 - y multiply by 2
0 > x - 1 - 2y
or x - 2y -1 < 0
Here is a desmos graph:
https://www.desmos.com/calculator/acwb5p136t
+36916 Find the equation of the line.......Is this the problem you are having?
+36916 OK...here ya go ( image below) Read carefully so you will understand .....
Pick two convenient points on the line.....see the ones I picked?
find the slope between these lines slope = m = (y1-y2)/(x1-x2) = (1-0) /( 3-1) = 1/2
so your line starts to look like y = mx + b <====== 'Slope-Intercept' form of a line
y = 1/2 x + b now we need to calculate 'b' use either of the points in the equation
using 3,1 1 = 1/2 (3) + b
b = - 1/2
Now your line equation is y = 1/2 x - 1/2
the shaded area of the graph is everything GREATER than ( above ) the line
y > 1/2 x - 1/2 then re-arrange it into the form needed ( as I did in earlier post ) ...... helpful?
+36916 Answer was shown in above post
x - 2y -1 < 0 <========= This is the form requested in the Q
