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

Guest Apr 18, 2021

#1**+1 **

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

ElectricPavlov Apr 18, 2021

#4

#5**0 **

Find the equation of the line.......Is this the problem you are having?

ElectricPavlov
Apr 18, 2021

#6

#7**+1 **

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?

ElectricPavlov
Apr 18, 2021

#8

#9**+1 **

Answer was shown in above post

x - 2y -1 < 0 <========= This is the form requested in the Q

ElectricPavlov
Apr 18, 2021