91Ó°ÊÓ

The slope of a line is a measure of how steep the line is. It is commonly represented by the letter "m." In mathematics, the slope is essentially the rate of change between any two points on a line.
It is calculated as the change in the vertical direction (rise) over the change in the horizontal direction (run).
The formula for calculating the slope between two points \[ (x_1, y_1) \quad \text{and} \quad (x_2, y_2) \]is:\[m = \frac{y_2 - y_1}{x_2 - x_1}\]When the slope is zero, like in this exercise, it indicates that there is no vertical change as you move along the line; hence, the line appears flat or perfectly horizontal.
A horizontal line means that the y-coordinate remains constant, regardless of the x-coordinate.

The slope-intercept form is a way of writing the equation of a line so you can easily identify its slope and y-intercept. This form uses the equation\[y = mx + b\]where:

• \(m\) represents the slope of the line
• \(b\) represents the y-intercept, which is the point where the line crosses the y-axis

This form is handy because it tells you how the line behaves just by looking at the equation. If the slope \(m\) is zero, like in this exercise, the formula simplifies. You're left with an equation \[y = b\]indicating a horizontal line.
Here, since it passes through the point \((6, 2)\), the equation becomes \(y = 2\).
This means every point on the line has a y-coordinate of 2.

Horizontal lines are simple yet special types of lines on the Cartesian plane. When a line is horizontal, it means the slope \(m\) is zero. This signifies no vertical movement or incline at all. A horizontal line runs parallel to the x-axis and stretches infinitely in both directions without changing its y-coordinate.
The equation of a horizontal line is always of the form \[y = b\]where \(b\) is the constant y-coordinate for all points along the line.
So, if you see an equation like \(y = 2\), you know it graphically represents a flat line where every point has a y-coordinate of 2.
This provides a visual representation of uniformity across the plane for that particular y-value.

The Cartesian plane is a two-dimensional surface that represents a space where every point is defined by two numbers: an x-coordinate and a y-coordinate. This system was named after the mathematician René Descartes, who developed this coordinate system.
It consists of two perpendicular lines or axes:

• The horizontal axis is called the x-axis.
• The vertical axis is called the y-axis.

On the Cartesian plane, any point is represented as \((x, y)\), showing its position in relation to the two axes.
When graphing lines, such as the horizontal line in our exercise, you make use of the Cartesian plane to visually plot where these points lie.
For a horizontal line like \(y = 2\), you would draw a straight line parallel to the x-axis at the constant y-coordinate of 2, showing an unchanging value across the plane.