Through (5,6) with slope -1 1/2

Question

Write the equation of the line that satisfies each of the given conditions

Answer 1

The point slope formula is y - y₁ = m(x - x₁), where (x₁, y₁) is the point you are given and m is the slope.  Note that I am going to convert the slope to an improper fraction.

y - y₁ = m(x - x₁)                    Point-slope formula

y - 6 = -3/2(x - 5)                   Substitution

y - 6 = -3/2x + 15/2                Distributive property

y - 6 + 6 = -3/2x + 15/2 + 6     Add 6 to each side

y = -3/2x + 15/2 + 6                Simplify the left side

y = -3/2x + 15/2 + 12/2           Find the common denominator

y = -3/2x + 27/2                     Simplify the right side