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Find a linear inequality with the following solution set. Each grid line represents one unit.
(Give your answer in "standard form"\( ax+by+c>0,or ,ax+by+c\geq0\) where $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)

 Jun 6, 2019

Best Answer 

 #1
avatar+8778 
+3

Start by finding the equation of the red line.

 

The red line passes through the points  (1, -2)  and  (3, 1)

 

slope of red line  =  \(\frac{\text{rise} }{ \text{run} }\ =\ \frac{1--2}{3-1}\ =\ \frac{3}{2}\)

 

Using the point  (1, -2)  and the slope  \(\frac32\) ,  the equation of the red line in point-slope form is:

 

y + 2  =  \(\frac32\)(x - 1)

                                 Multiply both sides of the equation by  2 .

2(y + 2)  =  3(x - 1)

                                 Distribute.

2y + 4  =  3x - 3

                                 Subtract  3x  from both sides and add  3  to both sides.

-3x + 2y + 7  =  0

 

And the red line is dotted, so it is not included in the inequality. So the liner inequality of the graph is either

 

-3x + 2y + 7  >  0       or       -3x + 2y + 7  <  0

 

To determine which one, pick a point which we know should make the inequality true and test that point.

 

We know that the point  (0, 0)  should make the inequality true.

 

Is it true that     -3(0) + 2(0) + 7  >  0       ?  Yes, it is true that  7 > 0 .

 

So the linear inequality of the graph is     -3x + 2y + 7  >  0

 

Check: https://www.desmos.com/calculator/er1ittpt1k

 Jun 6, 2019
 #1
avatar+8778 
+3
Best Answer

Start by finding the equation of the red line.

 

The red line passes through the points  (1, -2)  and  (3, 1)

 

slope of red line  =  \(\frac{\text{rise} }{ \text{run} }\ =\ \frac{1--2}{3-1}\ =\ \frac{3}{2}\)

 

Using the point  (1, -2)  and the slope  \(\frac32\) ,  the equation of the red line in point-slope form is:

 

y + 2  =  \(\frac32\)(x - 1)

                                 Multiply both sides of the equation by  2 .

2(y + 2)  =  3(x - 1)

                                 Distribute.

2y + 4  =  3x - 3

                                 Subtract  3x  from both sides and add  3  to both sides.

-3x + 2y + 7  =  0

 

And the red line is dotted, so it is not included in the inequality. So the liner inequality of the graph is either

 

-3x + 2y + 7  >  0       or       -3x + 2y + 7  <  0

 

To determine which one, pick a point which we know should make the inequality true and test that point.

 

We know that the point  (0, 0)  should make the inequality true.

 

Is it true that     -3(0) + 2(0) + 7  >  0       ?  Yes, it is true that  7 > 0 .

 

So the linear inequality of the graph is     -3x + 2y + 7  >  0

 

Check: https://www.desmos.com/calculator/er1ittpt1k

hectictar Jun 6, 2019

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