Question

Question #92c95

Answer 1

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 `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: