Graph the solution of each linear inequality.
y<2x-5? don't get it
Graph the straight line
y = 2x -5
Make y the vertical axis and x the horizontal axis (as is usually done).
Any point on the graph that is below the line will be a solution.
To graph the solution of the linear inequality y < 2x - 5, you can follow these steps:
Step 1: Start by graphing the boundary line. The boundary line is obtained by replacing the inequality symbol with an equal sign. In this case, the boundary line is y = 2x - 5.
Step 2: Plot the boundary line on a coordinate plane. To do this, you need to find two points on the line. One simple way is to assign random values to x and solve for y.
Let's choose x = 0:
y = 2(0) - 5
y = -5
So, the first point on the line is (0, -5).
Next, choose another value for x, such as x = 3:
y = 2(3) - 5
y = 1
The second point on the line is (3, 1).
Step 3: Plot the two points you found on the coordinate plane and draw a straight line through them. This line represents the boundary line of the inequality.
Step 4: Now, to determine which side of the line represents the solution to the inequality, choose a point not on the line and substitute its x and y-values into the original inequality. For example, you can use the origin (0, 0).
Substitute x = 0 and y = 0 into the inequality:
0 < 2(0) - 5
0 < -5
Since 0 is not less than -5, the origin is not a solution to the inequality. Therefore, this means the solution lies on the side of the line that doesn't include the origin.
Step 5: Shade the region below the boundary line to represent the solution to the inequality. This is done because the inequality is y < 2x - 5. The shaded region represents all the points that make the inequality true.
Here is an example graph of the solution:
```
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|
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+---------
| /
| /
| /
| /
+----------------------------------
```
The shaded area is below the line y = 2x - 5. This graph represents the solution to the inequality y < 2x - 5.