91Ó°ÊÓ

In mathematics, the slope-intercept form is one of the most common ways to represent a linear equation. The general form is given by: \( y = mx + b \)
Here, there are two main components:

• m: This represents the slope of the line, which defines how steep the line is.
• b: This is the y-intercept, which is the point where the line crosses the y-axis.

To understand the slope better, imagine moving from one point on the line to another. The slope is calculated as the 'rise' over the 'run,' or the change in y over the change in x. This helps in understanding the direction and inclination of the line.
For example, if a line's equation is \( y = 2x + 3 \), the slope \( m \) is 2, indicating that for each unit increase in x, y increases by 2 units. The y-intercept \( b \) is 3, meaning the line crosses the y-axis at y = 3.

One crucial step in solving or using equations is substituting given values into the equation. This helps to find unknown variables or verify a solution. Let's apply this to our current problem:
The given slope is 0. Inserting this into our slope-intercept form \( y = mx + b \), we get:\( y = 0x + b \).
This simplifies to:\( y = b \).
By doing this substitution, we've converted the general form into a simpler one by using the specific value provided for the slope. Substituting known values is a common technique you will often use in algebra and higher-level math.

Finding the y-intercept requires knowing a point through which the line passes and the slope. Often, the slope-intercept form helps in conveniently determining the y-intercept.
From our simplified equation, we already have \( y = b \).Given the problem, the line passes through (9,5). So, we substitute this into \( y = b \).
Thus, substituting x = 9 and y = 5:\( 5 = b \).
What does this mean? Our y-intercept \( b \) is 5. So, the line crosses the y-axis at y = 5. To write the final equation, substitute \( b \) back into the simplified equation to find:
\( y = 5 \).This is the final equation of the line, indicating that for any x-value, y will always be 5, creating a horizontal line through the y-axis at y = 5.