Problem 72 - Algebra A Combined Function

Question

Complete each ordered pair for the given equation. $$ y=-6 x+4 ;(0, \quad) $$

Step-by-Step Solution

Answer

The completed ordered pair is (0, 4).

Step 1: Understand the Equation Format

The given equation is in the form of a linear equation, where the expression involves two variables, x and y. This equation is written as follows: \( y = -6x + 4 \).

Step 2: Identify the Given Ordered Pair

You are provided with a partial ordered pair \((0, \_)\). This means you need to find the value of \( y \) when \( x = 0 \).

Step 3: Substitute the Value of x

Substitute \( x = 0 \) into the equation \( y = -6x + 4 \). This becomes \( y = -6(0) + 4 \).

Step 4: Simplify the Equation

Simplify the expression \( -6(0) + 4 \). Calculating this, we get \( 0 + 4 = 4 \).

Step 5: Complete the Ordered Pair

After substituting and simplifying, we find that \( y = 4 \) when \( x = 0 \). Thus, the completed ordered pair is \((0, 4)\).

Key Concepts

Ordered Pairs

When working with linear equations, an ordered pair is a pair of numbers used to locate a point on a graph. In the context of a linear equation like \( y = -6x + 4 \), an ordered pair \((x, y)\) represents one set of values that satisfy the equation. For any linear equation, each value of \( x \) corresponds to a value of \( y \), resulting in a point on the plane. Ordered pairs are commonly formatted as \((x, y)\).

• The first element (or coordinate) represents the value of \( x \).
• The second element represents the value of \( y \).

In the exercise, the given partial ordered pair is \((0, \_)\), meaning that we know the value of \( x \), and our task is to find the associated \( y \)-value.

Substitution Method

The substitution method is a technique used in algebra to find the values of variables in equations. With substitution, you plug in a specific value for one variable and solve for the other. This method is especially handy in solving linear equations where you have part of an ordered pair and need the rest.In the step-by-step solution, we used the substitution method by substituting the value of \( x = 0 \) into the equation \( y = -6x + 4 \). Once we substitute \( x \), the equation becomes \( y = -6(0) + 4 \), leaving us to only perform arithmetic operations to find \( y \). Using substitution helps to:

• Easily find missing values in ordered pairs.
• See how changes in one component affect the entire equation.

Simplifying Expressions

In algebra, simplifying expressions means breaking down complicated expressions into simpler or more manageable parts. This often involves performing arithmetic operations or combining like terms to make an expression easier to work with. After substituting \( x = 0 \) in the equation \( y = -6x + 4 \), we simplify it by performing the multiplication and addition:

• First, calculate \( -6 \times 0 \), which equals \( 0 \).
• Next, add \( 0 \) to \( 4 \), resulting in \( 4 \).

Therefore, the expression simplifies to \( y = 4 \). Simplifying expressions helps to clearly see the answer without unnecessary complexity, making it easier to identify the completed ordered pair, \((0, 4)\).