Question 172946
Two points determine a line, so that's all you need
The general equation for a line is
{{{y = mx + b}}}
This looks like a single equation with 4 unknowns, and
that is unsolvable, but the 2 points given will allow 
me to write 2 equations with 2 unknowns
given:
(3,7)
(2,-1)
(1) {{{7 = m*3 + b}}}
(2) {{{-1 = m*2 + b}}}
Now I solve for {{{m}}} and {{{b}}}
First, subtract (2) from (1)
{{{8 = m}}}
Now put this value for {{{m}}} back into (1)
{{{7 = 8*3 + b}}}
{{{b = 7 - 24}}}
{{{b = -17}}}
The equation of the line that passes trough (3,7) and (2,-1) is
{{{y = 8x - 17}}}
Now check the answer
(3,7)
{{{7 = 8*3 - 17}}}
{{{7 = 24 - 17}}}
{{{7 = 7}}}
OK
(2,-1)
{{{-1 = 8*2 - 17}}}
{{{-1 = 16 - 17}}}
{{{-1 = -1}}}
OK