This week in pre-calc, we learned how to graph linear inequalities. In order to be an inequality, there would need to be >,<, ≥ or ≤ in an equation, displaying that the numbers on each side do not perfectly equal each other like they would if it was =.

When graphing, we use a dotted line or a solid line to express the differences in signs used in an inequality

> – greater than (dotted line)  – doesn’t include boundary line (the line itself)

< – less than (dotted line) – doesn’t include boundary line

≥ – greater than or equal to – does include boundary line

≤ – less than or equal to – does include boundary line

With linear inequalities, the inequality must have a degree of 1 (no visible exponents). Such as, y>2x-2.

If we use this as an example, graphing the line is simple since we already know how to graph a line because we learned it in grade nine.

Now, adding what we just learned, we need to find on which side of the graph that y is greater than 2x-2 (y>2x-2). In order to do that, we test points on our graph. If they turn out true, we know that the side the point was on includes all true points that satisfy the inequality.

The easiest point to graph is (0,0) – insert it into the y and x places in our inequality.

y>2x-2

 

0>2(0)-2

 

0>-2

0 is greater than -2, so this statement is true. With this information we know that the side of the graph that this point was on is the side with all possible solutions. To express that, we shade in that side, making sure to have a dotted line to show that the points on the boundary line are not included because of the >.

With that, our graph expresses our inequality and we are done!