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.)

Guest Jun 6, 2019

#1**+2 **

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

hectictar Jun 6, 2019

#1**+2 **

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

hectictar Jun 6, 2019