How do I write an equation in slope intercept form, standard form, and point-slope form using two points (2,-5) and (7,12)?

First you find the , which is the amount ##y## changes for every increase of ##x##

Slope-intercept is of the form ##y=mx+b##

Slope= ##"change in y"/"change in x"## or more formally:

##m=(Deltay)/(Deltax)=(12-(-5))/(7-2)=17/5=3 2/5 or 3.4##

Now you know the slope, fill in what you know for one of the points:

##y=mx+b->-5=3 2/5 *2+b-> b=-11 4/5 or 11.8##

So the whole equation goes: ##y=3 2/5 x-11 4/5->y=3.4x-11.8##

Check with the other point:

##3.4*7 - 11.8 = 12## --check!