# How do you know how to shade the solution set of an inequality when the line is undefined?

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

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Almost line in the ##xy## plane can be expressed as ##y=mx+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 ##{(x > -2), (x <= 2), (y > 2x-1):}##

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

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