Find the slopes of the lines passing through the given points.

(1) Given A(2,3) and B(4,7)
x₁ = 2
y₁ = 3
x₂ = 4
y₂ = 7
Slope of the line AB = (y₂-y₁)/ (x₂-x₁)
= (7-3)/(4-2)
= 4/2 = 2
Hence Slope of line AB is 2.

(2) Given P(-3,1) and Q(5,-2)
x₁ = -3
y₁ = 1
x₂ = 5
y₂ = -2
Slope of the line PQ = (y₂-y₁)/ (x₂-x₁)
= (-2-1)/(5-(-3))
= -3/8
Hence Slope of line PQ is -3/8.

(3) Given C(5,-2) and D(7,3)
x₁ = 5
y₁ = -2
x₂ = 7
y₂ = 3
Slope of the line CD = (y₂-y₁)/ (x₂-x₁)
= (3-(-2))/(7-5)
= 5/2
Hence Slope of line CD is 5/2.

(4) Given L(-2,-3) and M(-6,-8)
x₁ = -2
y₁ = -3
x₂ = -6
y₂ = -8
Slope of the line LM = (y₂-y₁)/ (x₂-x₁)
= (-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)
x₁ = -4
y₁ = -2
x₂ = 6
y₂ = 3
Slope of the line EF = (y₂-y₁)/ (x₂-x₁)
= (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)
x₁ = 0
y₁ = -3
x₂ = 0
y₂ = 4
Slope of the line TS = (y₂-y₁)/ (x₂-x₁)
= (4-(-3))/(0-0)
= 7/0 = not defined
Hence Slope of line TS cannot be determined.