I am really confused...can someone help me with this? I am supposed to graph solution of given system of linear inequality:
y is greater than 4x-3
y is less than or equal to x+2
Consider the "equation" of the corresponding function, I will use yours as an example
y = 4x-3
Since it is a straight line, all you need are two points
since you had
y > 4x - 3, draw a dotted line to show that the points are excluded.
Shade in the region above that line
If the relation had been
y < 4x-3 , you would shade in the region below the line
If the relation had been ≥ or ≤ , you would make the boundary line solid, to show the points on the line would be included.
my explanation applies to all inequations of the form
y > f(x), y < f(x), y ≥ f(x), or y ≤ f(x)
Of course! I'd be happy to help you graph the solution of this system of linear inequalities.
To graph these types of inequalities, we need to consider each inequality separately and then combine their solutions.
Let's start with the first inequality, "y is greater than 4x-3."
To graph this inequality, we first need to identify the corresponding equation, which in this case is y = 4x - 3. This equation represents a straight line. To graph this line, we can start by plotting two points on the line.
To find these points, we can choose any values for x and substitute them into the equation to calculate the corresponding y values. For example, if we let x = 0, then y = 4(0) - 3 = -3. This gives us the point (0, -3). Similarly, if we let x = 1, then y = 4(1) - 3 = 1. This gives us the point (1, 1).
Plot these points on your graph, and then draw a straight line passing through them. This line represents the boundary of the "y is greater than 4x-3" inequality.
Next, let's move on to the second inequality, "y is less than or equal to x+2."
Again, we need to find the corresponding equation, which is y = x + 2. This equation also represents a straight line.
Similarly to before, let's choose values for x and calculate the corresponding y values. If we let x = 0, then y = 0 + 2 = 2. This gives us the point (0, 2). If we let x = 1, then y = 1 + 2 = 3. This gives us the point (1, 3).
Plot these points on the graph and draw a straight line passing through them. This line represents the boundary of the "y is less than or equal to x+2" inequality.
Now that we have graphed both inequalities individually, we need to find the region where the solutions of both inequalities overlap.
In this case, the shaded region below the first line (y > 4x-3) and below or on the second line (y ≤ x+2) represents the solution to the system.
To summarize, the solution to the system of linear inequalities is the shaded region that satisfies both inequalities.
I hope this explanation helps you to understand how to graph the solution of a system of linear inequalities! If you have any further questions, feel free to ask.