What is the equation of the line passing through #(2,17)# and #(1,-2)#?

First off, I am assuming that this equation is linear. Once I do that, I know that I can use the formula #y=mx+b#. The #m# is the slope and the #b# is the x-intercept. We can find the slope by using the #(y2-y1)/(x2-x1)#

Let's start by plugging in the information we have, like this:
#(-2-17)/(1-2)#, which simplifies to #(-19)/-1# or just #19#. That means the slope is #19#, and all we need is what #y# equals when #x# is #0#. We can do this by looking at the pattern.
#x##color(white)(..........)# #y#
2#color(white)(..........)# 17
#color(white)(................)#)+19
1 #color(white)(.......)# #-2#
#color(white)(................)#)+19
#color(red)(0)##color(white)(.......)##color(red)(-21)#

So, with this table I can tell that the #x#-intercept (when #x=0#, #y=?#) is #(0, -21)#. Now we know our #b# part of the equation.

Let's put it together:
#y=mx+b#
#y=19x-21#

Let's graph the equation we have and make sure it passes through the right points, #(2,17)# and #(1,-2)#
graph{y=19x+(-21)}

The graph fits those points so the equation is correct!