Graph x< 0 and y> 0
The question requires the creation of a graphical representation of a specific region on the Cartesian coordinate system. It specifies two inequality conditions:
x<0, which means that all x-values are less than zero, indicating the region is on the left side of the y-axis.
y>0, which means that all y-values are greater than zero, indicating the region is above the x-axis.
Together, these conditions define the quadrant of the Cartesian plane where both conditions are true. The question essentially asks for a visualization of this region, often by shading it. It is a basic exercise in understanding inequalities and their representation on a 2D graph.
$x < 0$and$y > 0$
Answer
Solution:
Step 1:
Plot the region where $x < 0$ and $y > 0$.
Step 2:
First, identify the vertical line $x = 0$. The area to the left of this line represents $x < 0$.
Step 3:
Next, find the horizontal line $y = 0$. The region above this line signifies $y > 0$.
Step 4:
The solution to the system of inequalities is the quadrant where both conditions are met, which is the second quadrant in the Cartesian coordinate system. Shade this quadrant to represent the solution.
Knowledge Notes:
To solve the problem of graphing the inequalities $x < 0$ and $y > 0$, we need to understand the Cartesian coordinate system and the concept of inequalities.
Cartesian Coordinate System: This system is a two-dimensional plane consisting of two perpendicular axes: the horizontal axis (x-axis) and the vertical axis (y-axis). The point where they intersect is called the origin, denoted as (0,0). The plane is divided into four quadrants.
Inequalities: An inequality is a mathematical statement that compares two values, showing if one is less than, greater than, or equal to another. In this case, $x < 0$ means that the value of x is less than zero, and $y > 0$ means that the value of y is greater than zero.
Graphing Inequalities: To graph an inequality, we first graph the corresponding equation (e.g., $x = 0$ for $x < 0$) and then determine which side of the line satisfies the inequality. For $x < 0$, we shade to the left of the line $x = 0$, and for $y > 0$, we shade above the line $y = 0$.
Quadrants: The Cartesian plane is divided into four quadrants. The second quadrant is where $x$ is negative, and $y$ is positive, which is the solution to the given inequalities.
By understanding these concepts, we can graph the solution to the inequalities by shading the appropriate region in the Cartesian plane.
