This week in Precalculus 11, we learned about graphing linear inequalities in 2 variables.

linear inequality: written in general form as ax + by + c </>/≤/≥ 0

To graph a linear inequality in 2 variables, we first graph its corresponding linear equation. To do this, we must rearrange the equation to standard form, where y = mx + b.

We then plot the y-intercept (b) and use the slope (m) to plot more points. We connect these points with a straight line. If the symbol is < or >, it means less than or greater than, and we use a broken line. If the symbol is ≤ or ≥, it means less than or equal to or greater than or equal to, and we use a solid line. 

One side of the line has solutions, and the other does not. To determine which side does, we plug a test point (labelled T) into the original equation. (0, 0) is a good test point. If the statement is true, we shade in the side of the graph with said point. If not, we shade in the other side.

This was interesting, as I had learned how to graph linear equations, but not inequalities.

Example: