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Chapter 3: Problem 9

The ordered pair \((4,___)\) is a solution of the equation \(y=3\)

Short Answer

Expert verified
The ordered pair is (4, 3).

Step by step solution

01

Understand the Equation

First, look at the given equation: \( y = 3 \). This tells us that the value of \( y \) is always 3, no matter what the value of \( x \) is.
02

Identify Given Coordinates

The ordered pair given is \((4, \text{___})\). Our goal is to find the second coordinate (\( y \)) in this pair.
03

Substitute and Solve

Since we know from Step 1 that \( y = 3 \), substitute \( y \) with 3 in the ordered pair. Therefore, the ordered pair is \((4, 3)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ordered Pairs
An ordered pair is a set of two numbers used to locate a point on a coordinate plane. The format is always \(x, y\), with \(x\) being the first coordinate and \(y\) the second. Think of it like an address: the \(x\) coordinate tells you how far to go left or right, and the \(y\) coordinate tells you how far to go up or down. For example, in the ordered pair \((4, 3)\), the number 4 tells us to move 4 units to the right, and the number 3 tells us to move 3 units up. This unique combination of numbers ensures we reach a specific point on the grid.
Substitution
Substitution is a method in algebra where you replace a variable with its actual value. In our example, the equation \(y = 3\) says that no matter what, \(y\) will always equal 3. Now, given the ordered pair \((4, ____)\), we need to find what \(y\) is when \(x\) is 4. By substituting \(y\) with 3 in the ordered pair, we get \((4, 3)\). This simple step solves the problem and finds the missing coordinate. The substitution method helps in solving more complex equations as well, making it a fundamental concept in math.
Solving Equations
Solving equations involves finding the value of the variable that makes the equation true. In simpler terms, it鈥檚 like finding the missing piece of a puzzle. For the equation \(y = 3\), solving it is straightforward because it already gives us the value of \(y\). Often, you will need to isolate the variable by performing arithmetic operations. These operations typically include:
  • Adding or subtracting terms on both sides of the equation
  • Multiplying or dividing by a number
If an equation is balanced, it means its left side equals its right side once the variable is properly replaced.
Coordinates
Coordinates are numbers that define a location on a grid, which is part of the coordinate plane. This plane has two axes: the x-axis (horizontal) and the y-axis (vertical). Each axis is a number line that helps you measure how far you need to go in each direction. The point where the axes intersect is called the origin, noted as (0, 0). In the pair (4, 3), 4 is the x-coordinate, telling you to move 4 units right. The 3 is the y-coordinate, telling you to move 3 units up. Using coordinates makes it easy to plot points and understand spatial relationships in geometry and many practical applications, such as navigation.

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Most popular questions from this chapter

Graph each linear equation. \(y=-\frac{3}{4} x+3\)

Graph each linear equation. \(y+3 x=0\)

For each pair of equations, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither. See Example \(6 .\) $$ \begin{aligned} 5 x-y &=1 \\ x-5 y &=-10 \end{aligned} $$

Plot each set of points, and draw a line through them. Then give the equation of the line. $$ (3,5),(3,0), \text { and }(3,-3) $$

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 3 y=-6 $$
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