# Question #92c95

Oct 17, 2016

Note that the slope of a line is undefined only when the line has the equation $x = c$, then proceed as usual.

#### Explanation:

Almost line in the $x y$ plane can be expressed as $y = m x + b$ where $m$ is the line's slope and $b$ is its $y$-intercept. The exception is when the slope of the line is undefined, that is, in the case of a vertical line.

A vertical line has an equation of the form $x = c$ for some constant $c$. If an inequality has such a line as a boundary, we simply pick whichever side of that line contains points satisfying the inequality and shade that, just as we would with a line that has a defined slope.

For example, here is the graph of $x < 3$:

In a system of inequalities, we just shade as normal for each inequality, and then keep wherever all of the shadings overlap.

If we have $\left\{\begin{matrix}x > - 2 \\ x \le 2 \\ y > 2 x - 1\end{matrix}\right.$

we would graph the three lines generated by equalities (remembering to used dashed lines for $>$ or $<$ and solid for $\ge$ or $\le$), and then keep the portion in which all three shaded areas overlap, giving us this: