Finding Slope of the Line Passing Through the Two Points

In the standard (x,y) coordinate plane, lines a and b intersect at point (5,-2) and lines b and c intersect at point (3,-3).  What is the slope of line b?
A.)  1/2
B.)  -5/2
C.)  -2/5
D.)  -5/8
E.)  It cannot be determined from the given information

If lines a and b intersect at point (5,-2) and lines b and c intersect at point (3,-3), then
line b passes through the points (5,-2) and (3,-3).

Find the slope of line b.

y2 - y1
--------- = slope
x2 - x1

Points (5,-2) and (3,-3) are (x1,y1) and (x2,y2).

-3 - (-2)
---------- = slope   {substituted given coordinates into slope formula}
  3 - 5

-3 + 2
--------- = slope   {simplified in numerator and denominator}
   -2

-1
---- = slope   {added in numerator}
-2

slope = 1/2   {simplified}

A.)  1/2

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