What is the equation of the line through (-1,0) (1,2)

First work out m the slope of the line 
m = rise / run =  (2-0) / 1-(-1) = 2 /2 = 1

equation is 
y - 2 = m(x - 1)

y - 2 = 1(x - 1)

y - 2 = x - 1

y = x - 1 + 2

y = x + 1

Your going to use the line equation (y = mx+b) passing through your two points. 

1. To do this first find your slope. The slope is going to be the m in your line equation.  Using the slope equation: 
slope= y2 -y1 / x2-x1 --> 2-0 / 1- (-1) = m = 1

2. Plug the slope into your y = mx+b equation and plug in one of your points to find b. 

i.e. y = 1x + b ---> 2 = 1 x 1 + b --> 2/1 = b =1 

Now put it all together: y = 1x + 1