Question

How do you graph the inequality `x + 2y <1`?

Answer 1

Isolate `y` into slope intercept form:

`2y < 1 - x`

`y <-1/2x + 1/2`

Now graph the line, using a dotted line (since the inequality symbol is `<` and not `≤`).

Select two test points, one on each side of the line.

Let Test Point 1 =(-1, 0)

`0 <^? -1/2(-1) + 1/2`

`0<^? 1/2 + 1/2`

`0< 1`

Hence, we shade to the left of the line, as shows the following graph of the inequality.

Note that if the first test point had not worked, we would have been able to immediately shade the right side of the line, by deduction.

Hopefully this helps!