+0  
 
0
67
2
avatar

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

Answer in standard notation

1. https://latex.artofproblemsolving.com/f/b/3/fb366296576fe86f9f1c3bf32bf77f860a26dd72.png

2.https://latex.artofproblemsolving.com/5/e/6/5e65ff3ab12a357e8cd5a5a29228a65b2e0e5fd7.png

Guest Dec 10, 2017
Sort: 

2+0 Answers

 #1
avatar+80874 
+2

For the first.....the points (1, -2) and (3,1) are on the graph

 

The slope between these is   [ 1 - - 2 ] / [ 3 - 1 ]  = 3/2

And the equation of the line connecting these points is

y  = (3/2)(x -1) - 2

y = (3/2)x -3/2 - 2

y  = (3/2)x - 7/2

 

Multiply through by 2

 

2y = 3x - 7      rearrange as

3x - 2y  = 7

Since we have a dashed line...we are going to have a "<" or ">" sign involved...put a point in the "yelllow"  into this equation to see which inequality sign we need.....(0,0) seems good

 

3(0) - 2(0)  =  7    ???

0  = 7       ???

And its clear that we need  the  "<"  sign

 

So.....the equation is

 

3x - 2y <  7

 

Here's the graph : https://www.desmos.com/calculator/vn7sb63doc

 

 

 

cool cool cool

CPhill  Dec 10, 2017
edited by CPhill  Dec 10, 2017
edited by CPhill  Dec 10, 2017
 #2
avatar+5888 
+1

Here's the second one:

 

The red line passes through the points  (0, 1)  and  (1, 0) , so

 

its slope  =  [ 0 - 1 ] / [ 1 - 0 ]  =  -1

 

Using the point  (0, 1)  and the slope  -1 ,  the equation of the red line is…

 

y - 1  =  -1x          Add  1  to both sides of the equation.
y  =  -x + 1           Add  x  to both sides of the equation.
x + y  =  1

 

We want the solutions to include all points to one side of the line, so the inequality will be either

 

x + y  ≤  1          or          x + y  ≥  1

 

The point  (0, 0) is in the yellow region, so we want  (0, 0)  to make the inequality true.

 

0 + 0  ≤  1          or          0 + 0  ≥  1
0 ≤ 1  true          or          0 ≥ 1  false

 

So the inequality that has  (0, 0) as a solution is the one we want, which is…


x + y  ≤  1

hectictar  Dec 10, 2017

13 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details