We want to simplify the given expression. To do it, we will use the Distributive Property. We will distribute

- 3

to the terms inside the parentheses.

- 3 (x - 5)

Distr

Distribute $- 3$

- 3 x - (- 3) 5

MultNegNegOnePar

$- a (- b) = a \cdot b$

- 3 x + 15

Since

- 3 x

and

15

are not like terms, the expression cannot be simplified further.

Extra

The Distributive Property and More

Let's recall the Distributive Property that we used in this exercise. In the book we are told that simplifying expressions such as the one form this exercise will help us prepare for the next chapter. The next chapter is about the point-slope form.

The Distributive Property

Multiplying a number by the sum of two or more addends produces the same result as multiplying the number by each addend individually and then adding all the products together.

a (b \pm c) (b \pm c) a = a \cdot b \pm a \cdot c = a \cdot b \pm a \cdot c

Note that the factor outside the parentheses is multiplied, or distributed, to every term inside. The Distributive Property is used to simplify expressions with parentheses.

Since the Distributive Property is an axiom, it does not need a proof.

Point-Slope Form

A linear equation with slope

m

through the point

(x_{1}, y_{1})

is written in the point-slope form if it has the following form.

y - y_{1} = m (x - x_{1})

In this equation,

(x_{1}, y_{1})

represents a specific point on the line, and

(x, y)

represents any point also on the line. Graphically, this means that the line passes through the point

(x_{1}, y_{1}) .

It is worth mentioning that the point-slope form can only be written for non-vertical lines. The point-slope form can be derived by using the Slope Formula. To do so,

(x, y)

— which represents any point on the line — is substituted for

(x_{2}, y_{2})

into the formula.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstituteII

$x_{2} = x$ , $y_{2} = y$

m = \frac{y - y _{1}}{x - x _{1}}

MultEqn

$LHS \cdot (x - x_{1}) = RHS \cdot (x - x_{1})$

m (x - x_{1}) = y - y_{1}

RearrangeEqn

Rearrange equation

y - y_{1} = m (x - x_{1})

Exercise