Write the equation for line ad, in standard form and slope-equation form

Let's find the slope first...(y2-y1)/(x2-x1)

m=(6-1)/(0--5)=5/5=1

y=x+b, using point (0,6)

6=0+b so b=5...

y=x+6

Standard form has both variables on one side and a constant on the other side and by convention the coefficient of x is positive so:

y-x=6

x-y=-6  This is standard form...

Now "slope equation" is murky...

There is the point-slope form:  (y-y1)=m(x-x1) which in this case is:

Using point (0,6)...

(y-6)=1(x-0)

y-6=x

And then there is slope intercept form which is y=mx+b, which we found earlier:

y=x+6