Are the following points solutions to $3x-y=1$?

1. $(-3, -10)$
2. $(-2,-7)$
3. $(-1, -4)$
4. $(0, -1)$
5. $(1, 2)$
6. $(2, 5)$
7. $(3, 8)$
8. $(0.5, 0.5)$

1. $(-0.5, -2.5)$
2. $(-1.5, -5.5)$
3. $(1.5, 3.5)$
4. $(2.5, 6.5)$
5. $(-2.5, -8.5)$
6. $(-\frac{1}{3},-2)$
7. $(\frac{1}{3},0)$

To graph any straight line, plot two points on the line and connect the dots.

Why do we do that? Why does it work?