I am having a hard time understanding these problems would some one please explain what i need to do the teacher is asking me for points on the graph i am totally confused
1)Graph the inequality.
y > –5
2)Solve the following system of linear inequalities by graphing.
Sure, I can help you understand these problems. Let's start with the first one:
1) Graphing the inequality y > -5:
To graph this inequality, you need to first understand what it means. The inequality y > -5 means that y can take any value greater than -5. So, we will have a line on the graph that represents y = -5, but the area above the line will be shaded because we want values of y that are greater than -5.
Here's how you can do it step by step:
Step 1: Draw a coordinate plane with x-axis and y-axis.
Step 2: Locate the line of y = -5 on the graph. This is a horizontal line passing through -5 on the y-axis.
Step 3: Since the inequality is y > -5, we need to shade the area above the line. You can do this by shading the region above the line (-5 on the y-axis) and extending it until it reaches the edge of the graph.
Now let's move on to the second problem:
2) Solving the system of linear inequalities by graphing:
To solve a system of linear inequalities by graphing, follow these steps:
Step 1: Write down the given inequalities. Let's say you have two inequalities, for example:
2x + y ≥ 4
x - y < 2
Step 2: Graph each inequality separately. To graph an inequality, first rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Then plot the y-intercept on the graph and use the slope to find one or two more points on the line. Finally, draw a line passing through these points.
Step 3: Once you have graphed both inequalities, look at the shaded regions on the graph. The solution to the system of inequalities is the overlapping region of the shaded areas. In other words, find the region where both inequalities are true.
If the shaded regions do not overlap, it means that there is no common solution to the system of inequalities.
I hope this explanation helps you in understanding and solving these problems. If you have any further questions, feel free to ask!