Which Is The Graph Of The Linear Inequality 6X + 2Y > 10?

September 09, 2023 Posting Komentar

Which is the graph of linear inequality 6x + 2y > 10? Brainly.ph from brainly.ph

If you are looking for a way to graph the linear inequality 6x + 2y > 10, you have come to the right place. In this article, we will explore how to graph this inequality step-by-step, so you can easily understand and apply it. Linear inequalities are essential in math and physics and are used to represent a region of a graph where a certain condition is met. In this case, we will be graphing the region where the equation 6x + 2y > 10 is satisfied.

Step-by-Step Guide to Graphing the Linear Inequality 6x + 2y > 10

Step 1: Solve for y

The first step in graphing the linear inequality 6x + 2y > 10 is to solve for y. To do this, we will begin by subtracting 6x from both sides of the inequality. This gives us:

2y > -6x + 10

Next, we will divide both sides of the inequality by 2 to isolate y:

y > -3x + 5

Step 2: Graph the Line y = -3x + 5

Now that we have solved for y, we can graph the line y = -3x + 5. To do this, we will begin by plotting the y-intercept, which is 5. We will then use the slope of -3 to find additional points on the line. To do this, we can move down 3 units and to the right 1 unit, then plot that point. We can repeat this process to find more points, or we can use a straight edge to connect the points we have found to draw the line.

Step 3: Shade the Region Above the Line

Now that we have graphed the line y = -3x + 5, we need to shade the region above the line to represent the inequality 6x + 2y > 10. To do this, we will select a point above the line and test it in the inequality. If the point satisfies the inequality, we shade the region that contains the point. If not, we shade the opposite region.

Let's select the point (0, 6) above the line y = -3x + 5. To test this point, we will plug in x = 0 and y = 6 into the inequality 6x + 2y > 10:

6(0) + 2(6) > 10

12 > 10

Since 12 is greater than 10, the point (0, 6) satisfies the inequality. Therefore, we shade the region above the line y = -3x + 5.

Step 4: Graph the Solution Region

Finally, we can graph the solution region, which is the region above the line y = -3x + 5 that satisfies the inequality 6x + 2y > 10. To do this, we simply shade the region above the line as we did in step 3.

Additional Tips for Graphing Linear Inequalities

Graphing linear inequalities can be tricky, but with a few additional tips, you can make the process much easier. Here are some tips to keep in mind when graphing linear inequalities:

Always solve for y first and graph the line.
Select a point above or below the line and test it in the inequality to determine which region to shade.
Use a dashed line for strict inequalities (such as < or >) and a solid line for non-strict inequalities (such as ≤ or ≥).
Remember that the solution region is the shaded region that satisfies the inequality.

Conclusion

Graphing linear inequalities is an essential skill in math and physics. To graph the linear inequality 6x + 2y > 10, we first solved for y and graphed the line y = -3x + 5. We then shaded the region above the line to represent the inequality 6x + 2y > 10 and graphed the solution region. By following these steps and keeping in mind the tips we discussed, you can easily graph any linear inequality and solve problems that involve them.

Remember, practice makes perfect! So, keep practicing graphing linear inequalities, and you will master this skill in no time.