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Find a linear inequality with the following solution set. Each grid line represents one unit.

(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.)

y > 1/2x - 1/2

y+x<=1

3x - 2y < 7

x+y-1>0

2x - 3y + 1 > 0

(3x - 7) / 2 > 0

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

Apr 18, 2021
#2
0

I dont really understand

Apr 18, 2021
#3
0

What part do you not understand? ElectricPavlov  Apr 18, 2021
#4
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How do I answer it? Like what are the steps to answer it?

Apr 18, 2021
#5
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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
0

So that means x < 2y+1 is the answer? Am i correct?

Apr 18, 2021
#9
+1

Answer was shown in above post

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

ElectricPavlov  Apr 18, 2021