Question 165172
One way to do it (not the only way) is this:
Write the general slope-intercept equation
{{{y = mx + b}}} where {{{m}}} is the slope
and {{{b}}} is the y-intercept
The line in the problem passes through
(5,2) and (-7,3)
Substitute the 1st point in the general equation
(1) {{{2 = 5m + b}}}
Substitute the 2nd point in the general equation
(2) {{{3 = -7m + b}}}
You have 2 unknowns and 2 equations, so it's solvable
Subtract (1) from (2)
{{{1 = -12m}}}
{{{m = -(1/12)}}}
Substitute this in (1)
{{{2 = -(5/12) + b}}}
{{{b = 24/12 + 5/12}}}
{{{b = 29/12}}}
Now plug {{{m}}} and {{{b}}} back into the general equation
{{{y = -(1/12)x + 29/12}}} answer
Check to see if the line passes through (5,2) and (-7,3)
{{{2 = -(1/12)*5 + 29/12}}}
{{{24 = -5 + 29}}}
{{{24 = 24}}}
and
{{{3 = -(1/12)*(-7) + 29/12}}}
{{{36 = 7 + 29}}}
{{{36 = 36}}}
OK