Question 46532
The 2 points alone will give you the slope.
{{{m = (y(2) - y(1)) / (x(2) - x(1))}}} where m is the slope.
The points given are in the form
(2,5) = x(2), y(2) and
(7, -3) = x(1), y(1))
so
{{{m = (5 - (-3)) / (2 - 7)}}}
{{{m = 8 / -5}}}
{{{m = -(8/5)}}}
Now you need something that equals the slope, but is 
general in form and applies to any x or y.
{{{m = (y - y(1)) / (x - x(1))}}}
This is perfectly true as long as x and y are on the line passing
through (2,5) and (7,-3). To make that so, set it equal to the
value of m you got from {{{m = (y(2) - y(1)) / (x(2) - x(1))}}}
{{{-(8/5) = (y - y(1)) / (x - x(1))}}}
{{{-(8/5) = (y - (-3)) / (x - 7)}}} 
Now you can put it in the form y = mx + b
multiply both sides by (x - 7)
{{{-(8/5)*x + (56/5) = y + 3}}}
{{{-8x + 56 = 5y + 15}}}
{{{5y = -8x + 41}}}
{{{y = -(8/5)x + 41/5}}} this is the answer
The slope m is correct. Check to see if b = 41/5 is correct by setting
x = 0 in the slope formula
{{{-(8/5) = (y - (-3)) / (0 - 7)}}}
{{{56/5 = y + 3}}}
{{{y = 56/5 - 3}}}
{{{y = 56/5 - 15/5}}}
{{{y = 41/5}}}
checks OK