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Chapter 4: Problem 1

In the ordered pair \((4,9),\) the \(x\) -coordinate is ______ $

Short Answer

Expert verified
The x-coordinate is 4.

Step by step solution

01

Understand ordered pairs

We need to understand that an ordered pair is expressed as (x, y), where 'x' represents the x-coordinate (distance along the horizontal axis) and 'y' represents the y-coordinate (distance along the vertical axis).
02

Identify the x-coordinate

In our given ordered pair (4,9), the x-coordinate is the first number, which is 4.

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Key Concepts

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

x-coordinate
The x-coordinate in an ordered pair is the first value listed. It tells you how far to move horizontally across the coordinate plane from the origin, which is the point (0,0).
  • Think of the x-coordinate as the number of steps you take sideways, left or right.
  • In the ordered pair (4, 9), the x-coordinate is 4.
  • This means starting from the origin, you move 4 steps to the right.
Moving horizontally is a key idea in working with coordinates. Always remember: first comes x, then comes y. This is why it's essential to check the order to avoid any mix-ups.
Understanding this helps you place points accurately on a graph every time.
y-coordinate
The y-coordinate in an ordered pair is the second value. This tells you how far to move vertically from the x-coordinate you have already defined.
  • Imagine the y-coordinate as steps you move up or down from the position on the x-axis.
  • In the ordered pair (4, 9), the y-coordinate is 9.
  • From the x-position (4 on the x-axis), you move 9 steps upwards.
This vertical direction is crucial for pinpointing exact locations on a coordinate plane.
Unlike the x-coordinate, which moves sideways, the y-coordinate allows you to navigate upwards and downward. This dual movement creates a grid that lets you chart any point accurately.
coordinate plane
A coordinate plane, also known as a Cartesian plane, is like a map where you can locate points using ordered pairs.
  • The plane consists of two perpendicular lines: the x-axis (horizontal) and the y-axis (vertical).
  • Where they intersect is called the origin, labeled as (0,0).
  • The plane is divided into four sections called quadrants, helping you to categorize and find points easily.
Each point on the plane is determined by a pair of numbers: the x-coordinate and the y-coordinate.
This sometimes intimidating grid becomes simple when you realize it's just a system to help us say exactly where something is. Learning how to navigate it, using ordered pairs, opens up a world of problem-solving abilities in math and beyond.

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Most popular questions from this chapter

Use the following information. Your school drama club is putting on a play next month. By selling tickets for the play, the club hopes to raise \(\$ 600\) for the drama fund for new costumes, scripts, and scenery for future plays. Let \(x\) represent the number of adult tickets they sell at \(\$ 8\) each, and let \(y\) represent the number of student tickets they sell at \(\$ 5\) each. What are three possible numbers of adult and student tickets to sell that will make the drama club reach its goal?

Plot and label the ordered pairs in a coordinate plane. $$A(3,-5), B(1.5,3), C(-3,-1)$$

Graph the two lines in the same coordinate plane. Then find the coordinates of the point at which the lines cross. \(x=-5, y=2\)

Solve the equation. $$ 5(w-5)=25 $$

Describe a line that cannot be the graph of a linear function.
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