Graph y<-x+2
y < 2
x < 2
Graph the line y = -x+2
Then shade the area below the line (where y < -x+2)
Make the line a dashed line, to show that the boundary is not included in the solution.
To graph the equation y < -x + 2, we need to plot the points that satisfy this inequality.
Step 1: Start by drawing a coordinate plane, with the x-axis and y-axis intersecting at the origin (0,0).
Step 2: Let's begin plotting some points. To find the points that satisfy the inequality y < -x + 2, we can substitute different values of x into the equation and find the corresponding y-values.
Let's choose three arbitrary x-values and solve for their y-values:
When x = 0:
y = -(0) + 2
y = 2
So, we have the point (0, 2) on the graph.
When x = 1:
y = -(1) + 2
y = 1
So, we have the point (1, 1) on the graph.
When x = -1:
y = -(-1) + 2
y = 3
So, we have the point (-1, 3) on the graph.
Step 3: Plot these points on the coordinate plane.
Step 4: Now, we need to determine how to shade the region that satisfies the inequality y < -x + 2. To do this, we can choose a test point not on the graph, such as (0,0), and substitute its coordinates into the inequality.
When we substitute x = 0 and y = 0, we get:
0 < -(0) + 2
0 < 2
Since this statement is true, we shade the region below the line.
Step 5: Connect the plotted points with a dashed line to represent the inequality y < -x + 2.
The graph of y < -x + 2 is a dashed line below the line connecting the points (0, 2), (1, 1), and (-1, 3).