How do you graph the inequality #y>= x+5 #?

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

We can now plot the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality. The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-5)^2-0.125)((x+2)^2+(y-3)^2-0.125)(y-x-5)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

graph{(y-x-5) >= 0 [-20, 20, -10, 10]}

To graph the inequality (y \geq x + 5), follow these steps:

1. Graph the line (y = x + 5) as if it were an equation.
2. Since the inequality is greater than or equal to, the region above the line is shaded.
3. Draw a dashed line to represent (y = x + 5) because the inequality does not include the line itself.
4. Shade the area above the dashed line to represent the solutions to the inequality.

This creates a shaded region above the line, indicating all the points that satisfy the inequality (y \geq x + 5).