91Ó°ÊÓ

When we talk about parallel lines in geometry, we refer to lines that never intersect. They maintain a constant distance between each other, regardless of how far they extend.
An important property of parallel lines is that they have identical slopes.
The slope is a measure of the steepness or incline of a line. If Line A is parallel to Line B, then Line A and Line B have the same slope. For instance, in the given exercise, we have the line equation \(y = 0.5x - 9\). Any line parallel to this line will also have a slope of 0.5, just as the given line does.

The slope-intercept form is a way of expressing a linear equation. The general form is \(y = mx + b\), where:

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

In the exercise, our equation is \(y = 0.5x - 9\):

• Here, \(m = 0.5\), so the slope of the line is 0.5.
• The y-intercept, \(b\), is -9, meaning the line intersects the y-axis at (0, -9).

Being familiar with this form makes it easy to identify both the slope and the y-intercept of any linear equation, simplifying the process of graphing it or understanding its properties.

The equation of a line represents all the points that lie on that line in the coordinate plane. There are several forms to represent this equation, with the slope-intercept form being one of the most common.
To recap, the slope-intercept form is written as \(y = mx + b\).
Other forms include the point-slope form \(y - y1 = m (x - x1)\), where \(m\) is the slope and \((x1, y1)\) is a specific point on the line.
Understanding these forms is crucial for tasks like finding the slope, identifying parallel and perpendicular lines, and graphing.
In our exercise, we specifically worked with the slope-intercept form, making it straightforward to determine that any line parallel to \(y = 0.5x - 9\) will have the same slope of 0.5.