Math 1 · Unit 5 · Lesson 1 · part 2 of 6
An equation gives a line, an inequality gives a region
In Unit 3, an equation like y = 2x + 1 was made true by the points on one line, and only those points.
An equation gives a line, an inequality gives a region
In Unit 3, an equation like y = 2x + 1 was made true by the points on one line, and only those points. Feed in any x, get the one y, and that point sits on the line. Every point off the line makes the equation false.
Now change one symbol: y > 2x + 1. Read it: y is greater than 2x + 1. The gator eats the bigger number, and y is the bigger one. This is not made true by a line. Take x = 1: the line has y = 3 there, and the inequality wants y bigger than 3, so (1, 4), (1, 5), (1, 100) all work. Every x has a whole tower of solutions above the line. Put the towers together and you get a region: one entire side of the line, called a half-plane.