(1) Given A(2,3) and B(4,7)

x_{1} = 2

y_{1} = 3

x_{2} = 4

y_{2} = 7

Slope of the line AB = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (7-3)/(4-2)

= 4/2 = 2

Hence Slope of line AB is 2.

(2) Given P(-3,1) and Q(5,-2)

x_{1} = -3

y_{1} = 1

x_{2} = 5

y_{2} = -2

Slope of the line PQ = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (-2-1)/(5-(-3))

= -3/8

Hence Slope of line PQ is -3/8.

(3) Given C(5,-2) and D(7,3)

x_{1} = 5

y_{1} = -2

x_{2} = 7

y_{2} = 3

Slope of the line CD = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (3-(-2))/(7-5)

= 5/2

Hence Slope of line CD is 5/2.

(4) Given L(-2,-3) and M(-6,-8)

x_{1} = -2

y_{1} = -3

x_{2} = -6

y_{2} = -8

Slope of the line LM = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (-8-(-3))/(-6-(-2))

= -5/-4 = 5/4

Hence Slope of line LM is 5/4.

(5) Given E(-4,-2) and F(6,3)

x_{1} = -4

y_{1} = -2

x_{2} = 6

y_{2} = 3

Slope of the line EF = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (3-(-2))/(6-(-4))

= 5/10 = 1/5

Hence Slope of line EF is 1/2.

(6) Given T(0,-3) and S(0,4)

x_{1} = 0

y_{1} = -3

x_{2} = 0

y_{2} = 4

Slope of the line TS = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (4-(-3))/(0-0)

= 7/0 = not defined

Hence Slope of line TS cannot be determined.