Which Is The Graph Of The Linear Inequality 2Y X-2?
Welcome to our blog post for the year 2023. Today, we will be discussing the topic of graphing linear inequalities. Specifically, we will focus on the inequality 2y x-2 and how to graph it.
What is a Linear Inequality?
Before we dive into the specifics of graphing the inequality 2y x-2, let us first define what a linear inequality is. A linear inequality is an inequality where the variables are only raised to the first power and the inequality sign (<, >, ≤, ≥) is used to compare two expressions. For example, 3x + 2y ≤ 7 is a linear inequality.
Graphing Linear Inequalities
Graphing linear inequalities involves plotting the solutions of the inequality on a coordinate plane. The solutions can be found by testing points on either side of the inequality line. If the point satisfies the inequality, it is shaded on the graph. If not, it is left unshaded.
Step-by-Step Guide to Graphing 2y x-2
Now that we understand the basics of linear inequalities and graphing, let's dive into the specifics of graphing 2y x-2. Here are the steps:
Let's go through each of these steps in detail:
Step 1: Solve for y
To graph the inequality 2y x-2, we need to first solve for y.
2y x-2
2y ≤ -x + 2
y ≤ (-1/2)x + 1
Step 2: Plot the y-intercept
The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x equal to 0 and solve for y.
y = (-1/2)(0) + 1
y = 1
So, the y-intercept is the point (0,1).
Step 3: Plot the x-intercept
The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y equal to 0 and solve for x.
0 = (-1/2)x + 1
x = 2
So, the x-intercept is the point (2,0).
Step 4: Draw the line through the intercepts
Using the two intercepts we found in steps 2 and 3, we can draw a line through them.
Graph:
Step 5: Test a point on either side of the line
To determine which side of the line to shade, we need to test a point on either side of the line. One convenient point to test is the origin (0,0).
y = (-1/2)x + 1
y = (-1/2)(0) + 1
y = 1
Since (0,0) is above the line, we shade the region above the line.
Step 6: Shade the appropriate region
Now that we know which side of the line to shade, we can shade the appropriate region.
Graph:
Conclusion
In conclusion, graphing linear inequalities involves plotting the solutions of the inequality on a coordinate plane. To graph the inequality 2y x-2, we first solved for y and found the intercepts of the line. We then drew the line through the intercepts and tested a point on either side of the line to determine which side to shade. The appropriate region was then shaded.
Remember, when graphing linear inequalities, it is important to always check your work and test your solution points!
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