Graph inequality.
y is < or equal to -x+2
To graph the inequality y ≤ -x+2, we will follow these steps:
Step 1: Begin by graphing the equality y = -x+2.
- To graph this equation, we need two points on the line. We can find these points by choosing two arbitrary values for x and substituting them into the equation to find the corresponding y values.
Let's choose x = 0:
- Plug x = 0 into the equation: y = -0 + 2
- Calculate y: y = 2
So, our first point is (0, 2).
Let's choose x = 2:
- Plug x = 2 into the equation: y = -2 + 2
- Calculate y: y = 0
So, our second point is (2, 0).
Now, plot these two points on the graph.
Step 2: Draw the line connecting the two points.
- Use a straightedge to draw a line passing through the two points you plotted. This is the graph of the equation y = -x+2.
Step 3: Shade the area below the line to represent the inequality y ≤ -x+2.
- Since the inequality is y ≤ -x+2, we need to shade the area below the line we just drew.
- Use a pencil or a pen to shade the region below the line.
Finally, label the graph and write the inequality symbol (≤) above the line.
The resulting graph should have a solid line that represents the equation y = -x+2, and the area below the line should be shaded.