Question 6477
First step is to find the slope between the two points.
{{{m=(y[2] - y[1])/(x[2]-x[1])}}}


In this case,
{{{m=(-1-7)/(5-(-3))= (-8)/8 = -1}}}


There are two ways to find the equation of a line given a point and a slope.  This may NOT be the way you learned it, but I think the easiest way is to write the formula {{{y = mx+b}}}, which contains a total of 4 unknowns: y, x, m, and b, of which you know three of them--all but b, which you will need to find.  You know that m = -1, and you know a point (choose either point, say the first point):  x=-3 and y=7.  So substitute all three numbers into the equation: 


{{{y=mx+b}}}
{{{7 =(-1)*(-3) + b}}}


and solve for b:
{{{7 = 3 + b}}}
{{{4 = b}}}


So the equation of the line is 
{{{y=mx+b}}} where x and y are variables and m= -1 and y = 4:
{{{y = -x + 4 }}}