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 $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)

A linear inequality is an expression which make comparison between linear expressions using inequalities. The linear inequality of the graph is:

First, we calculate the slope of the dashed line using:

Two points on the graph will be:

The slope (m) is:

The equation of the line is calculated as:

So, we have;

Multiply through by 2

Now, we convert the equation to an inequality.

The line on the graph is a dashed line. This means that the inequality is either > or <. Also, the upper region of the graph that is shaded means that the inequality  is >.

So, the equation becomes

Rewrite as:

So, the linear inequality is:

Learn more about linear inequality at:

link

-x + 2y + 1 > 0

Step-by-step explanation:

Let's find the equation of the dashed line first. From the graph, we can see that it has a slope of 1/2 and a y-intercept of -1/2 so using slope-intercept form, the equation of the line is y = 1/2x - 1/2. Since the line is dashed and not solid, we know that we will use either < or > instead of ≤ or ≥, and because we can see that the shaded region is above the dashed line, we know that the linear equation is y > 1/2x - 1/2. However, we want the answer to be in the form ax + by + c > 0 where a, b, and c are integers so therefore:

y > 1/2x - 1/2

= 2y > x - 1

= -x + 2y + 1 > 0

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2