The slope m of a non vertical line through any two points is given by,

Substitute  for m, r for x₁, 5 for y₁, 2 for x₂ and r for y₂ in slope form.

Apply cross products property: If then .

Distribute terms using distributive property: .

                  (Product of two same signs is positive)

                     (Multiply: )

Apply addition property of equality: If a = b then a + c = b + c.

      (Add 45 to each side)

                     (Apply additive inverse property: )

Apply commutative property of addition: a + b = b + a.

                          (Add: 4 + 45 = 49)

Apply subtraction property of equality: If a = b then a c = b c.

            (Subtract 2r from each side)

Apply commutative property of addition: a + b = b + a.

                          (Apply additive inverse property: )

                                 (Subtract: )

Apply division property of equality: If a = b then .

                            (Divide each side by 7)

                                (Cancel common terms)

                                    (Divide: )

The value of .