The first thing we want to do is to find the slope between these two points. The equation for the slope, m, is:
Let the first point (-1,0)=(x1,y1) and the second point (1,2)=(x2,y2), then
m=(2-0)/(1-(-1))=2/2=1, so the slope between these two points is 1.
Now, we can write the equation of the line in point-slope form, where m is the slope:
y-0=1(x+1) or y=1(x+1), which is the equation of the line in point-slope form. Note: Instead of (x1,y1), you could also use (x2,y2). Your point-slope form equation will then look like: y-2=1(x-1), which will still give you the same equation for the slope-intercept form once you rearrange the equation.
The equation for slope-intercept form is, where m is the slope and b is the y-intercept:
So we just want to rearrange our equation of the line in point-slope form so that it looks like the equation of the line in slope-intercept form. To do that, we re-write y=1(x+1) as:
y=1x+1 where the 1 was distributed through the parenthesis. So the equation of the line in slope-intercept form is:
And for this equation, we see that b=1, so the equation goes through the y-axis at y=1.
Hope that helps!