First, consider the characteristics of the line. The slope is equal to 2 and the y-intercept is equal to 3. Because the line is solid, that indicates that the inequality is "greater than or equal to" or "less than or equal to". Finally, choose a point to determine the direction of the shading. The origin (0,0) is usually a good choice unless it falls on the line. If the chosen point makes the statement true, it must be included in the shaded region. If it is false, it must not.

Because 0 is less than 3 and the origin is not included in the shaded region, the correct answer must include "greater than or equal to"

In order to graph the inequality pictured above, we must first find the equation of its boundary line. Based on the image, we see that the line includes the points  and , so the slope of the line is

.

We can now find the -intercept form of the line by substituting  and the point   into the slope-intercept equation  and solving for :

The equation of the boundary line is therefore . Since we see that the boundary line is dashed, we know that the values on the line are excluded from the inequality, so the  sign will be replaced by a  or a .

In order to determine which one, we can test a point in the solution set; let's test  since it's the simplest to substitute:

 _____

 _____

 _____

, so the correct symbol is : 

In order to graph the inequality pictured above, we must first find the equation of its boundary line. Based on the image, we see that the line includes the points  and , so the slope of the line is

.

We can now find the -intercept form of the line by substituting  and the point   into the slope-intercept equation  and solving for :

The equation of the boundary line is therefore . Since we see that the boundary line is solid, we know that the values on the line are included in the inequality, so the  sign will be replaced by a  or a .

In order to determine which one, we can test a point in the solution set; let's test  :

 _____

 _____

 _____

, so the correct symbol is : 

In order to graph the inequality pictured above, we must first find the equation of its boundary line. Based on the image, we see that the line includes the points  and , so the slope of the line is

.

We can now find the -intercept form of the line by substituting  and the point   into the slope-intercept equation  and solving for :

The equation of the boundary line is therefore . Since we see that the boundary line is dashed, we know that the values on the line are excluded from the inequality, so the  sign will be replaced by a  or a .

In order to determine which one, we can test a point in the solution set; let's test  :

 _____

 _____

 _____

, so the correct symbol is :