How do you Draw the graph of y is greater than or equal to -x plus 5?

Answer 1

(1) First draw the line y = -x + 5.

To do that, find two points that lie on the line. Well, when x = 0, y = 5, so plot (0,5) on the plane. When x = 1, y = 4, so plot (1,4). Now draw the only straight line that goes through both of those points. Because the inequality allows for points to lie on the line itself (that's the "or equals to" part), you can make the line solid. If it were just "greater than" (and not equals to) you would draw a dotted line.

(2) Shade the correct side of the line.

This line divides the plane in two. One side is all the points that satisfy the inequality; on the other side of the line none of the points satisfy the inequality. We will shade in the side that satisfies the inequality. To figure out which side it is, pick a point not on the line, like (0,0). Plug it into your inequality:

y >= -x + 5

0 >= 0 + g

0 >= 5

This is not true, so shade the side of the plane that does not contain the origin.