In Exercises 1-12, plot the given point in a rectangular coordinate system. (1, 4)

Verified step by step guidance

1. Step 1: Understand the rectangular coordinate system, which consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical).
2. Step 2: Identify the given point (1, 4), where 1 is the x-coordinate and 4 is the y-coordinate.
3. Step 3: Locate the x-coordinate on the x-axis. Move 1 unit to the right from the origin (0, 0) since the x-coordinate is positive.
4. Step 4: From the point (1, 0) on the x-axis, move vertically upwards 4 units to reach the y-coordinate, since the y-coordinate is positive.
5. Step 5: Mark the point (1, 4) on the graph where the x-coordinate 1 and the y-coordinate 4 intersect.

Key Concepts

Rectangular Coordinate System

A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. This system allows for precise plotting of points and is fundamental in algebra and geometry.

Ordered Pairs

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y). The first number, 'x', corresponds to the horizontal distance from the origin along the x-axis, while the second number, 'y', represents the vertical distance along the y-axis. The order of the numbers is crucial, as switching them would indicate a different point in the coordinate plane.

Plotting Points

Plotting points involves marking a specific location on the coordinate plane based on its ordered pair. To plot the point (1, 4), you start at the origin (0, 0), move 1 unit to the right along the x-axis, and then move 4 units up along the y-axis. This visual representation helps in understanding relationships between variables and is essential for graphing functions and data.