A line passes through the given points (-1,0),(1,2). Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form.

The first thing we want to do is to find the slope between these two points. The equation for the slope, m, is:

m=rise/run=(y_{2}-y_{1})/(x_{2}-x_{1}).

Let the first point (-1,0)=(x_{1},y_{1}) and the second point (1,2)=(x_{2},y_{2}), 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-y_{1}=m(x-x_{1})

y-0=1(x-(-1))

y-0=1(x+1) or y=1(x+1), which is the equation of the line in
point-slope form. *Note: Instead of (x _{1},y_{1}), you could also use (x_{2},y_{2}). 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:

y=mx+b

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:

y=x+1

And for this equation, we see that b=1, so the equation goes through the y-axis at y=1.

Hope that helps!