91Ó°ÊÓ

A coordinate plane is like a grid that helps us find and plot points using a pair of numbers. These numbers are called coordinates, and they are written as you guessed it - (x, y)!
Each point on the plane has an x-coordinate, which tells us how far to move right or left, and a y-coordinate, which tells us how far to move up or down.
The plane is divided into four sections called quadrants, created by two intersecting lines:

• The horizontal line, called the x-axis.
• The vertical line, called the y-axis.

The point where the axes meet is the origin, marked as (0, 0).
Understanding how to locate and plot points on a coordinate plane is the foundation for graphing any equation. It's like finding a treasure map that tells you exactly where to go! Think of points as locations that, once plotted, can show the shape or trend of an equation.

The slope is a number that tells us how steep a line is on the coordinate plane. It gives a sense of how quickly a line moves upwards or downwards.
For the equation \( y = -2x \) used in the exercise, the slope is represented by the number -2.
Here's what slope tells us:

• A positive slope means the line goes up from left to right.
• A negative slope means the line goes down from left to right. In our equation, the negative slope of -2 creates a line that slopes downward.
• A larger absolute value of slope means a steeper line. So, a slope of -2 is steeper than a slope of -1.
• A slope of zero means a flat horizontal line.

When we say the slope is -2, it also means for every 1 unit we move right (increasing x), we move down 2 units on the y-axis. Understanding slope is key to predicting where a line will go.

Graphing equations is a way to visually represent equations on the coordinate plane. To graph our equation \( y = -2x \), we use points that satisfy the equation.
Here's a simple way to graph:

• Select some x-coordinates. In our example, we chose -1, 0, and 1.
• Calculate the corresponding y-coordinates by plugging the x-values into the equation. For \( y = -2x \):
  - At \( x = -1 \), \( y = 2 \).
  - At \( x = 0 \), \( y = 0 \).
  - At \( x = 1 \), \( y = -2 \).
• Plot these points on the coordinate plane: (-1, 2), (0, 0), and (1, -2).
• Connect the points with a straight line.

The line you draw captures all solutions to your equation, giving you a clear visual of how x and y relate. This method of graphing helps solve problems and understand the behavior of linear equations.