Find the equation of the line containing the given points. Write the equation in​ slope-intercept form, if possible. Graph the line? (-2,7); (1,-8)

First off, slope-intercept form is #y=mx+b#
#x# and #y# are both coordinates for a given point such as (-2,7) and (1,-8)

#m# is the slope of the line which is "rise over run" or the change in #y# divided by the change in #x#.

So our first step is to get m by using our two coordinates by subtracting one #y# from the other and subtracting the coordinating #x# from the other #x#. This means that there is no necessary way to pick which #y# to subtract from which, but as long as you use one coordinate set to subtract the other, you'll be ok.

For our case we would have either
#(7- -8)/(-2-1)# or #(-8-7)/(1--2)#
the double negatives turn into pluses and the answers are
#15/-3# or #(-15)/3#
Either way, the answer is #-5# for #m#

so now that we know our #m# and we are given possible #x,y# pairs, we can solve for #b#.

We do this by inserting one of our coordinate sets into the equation
#(-2,7)# as #7=-5*-2 +b#
#(1,-8)# as #-8=-5*1 +b#

If we solve for #b# by multiplying #m# by #x# then subtracting that number from #y#, we should have #b#.

#7=-5*-2+b#
#7=10+b#
#-3=b#

#-8=-5*1+b#
#-3=b#

We can get #b# through either coordinate and it will be the same.

Lastly, we put all the information together to get:
#y=-5x-3# as our answer

The simple way to graph a line given by two coordinates is to graph out each one and drawing a line between the two. We really don't need the equation to do so, but it helps us double check our line (especially at #+b# which is where the line crosses the #x# axis.

If you need more help with this part, ask and I can add more.
graph{y=-5x-3 [-10, 10, -5, 5]}
should look like this though