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

1 Answer
Apr 3, 2015

First you find the slope, 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!