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The slope-intercept form is a way of writing the equation of a line. It's one of the most common and easiest forms to understand. This form is given by the equation: \( y = mx + b \)In this equation:

• \(m\) is the slope of the line, which tells you how steep the line is.
  
• \(b\) is the y-intercept, which is where the line crosses the y-axis.

The slope-intercept form is incredibly useful because it gives you a quick way to get a visual sense of the line on a graph. All you need are the slope and the y-intercept, and you can easily draw the line.Let’s break this down further using the example in the exercise. Given the slope is \(0\), which means our line is horizontal.

A linear equation represents a straight line on a graph. The general form of a linear equation is typically written as \( Ax + By = C \)However, in slope-intercept form, it’s written as:\( y = mx + b \).This type of equation makes it easier to find important characteristics of the line, such as its slope and y-intercept. In our exercise, we are given the slope \( m = 0 \), simplifying our equation to \( y = b \).This tells us that the value of the line’s y-coordinate is constant, regardless of the x-coordinate. Essentially, this leads us to understand that the graph is a horizontal line. It’s a straightforward yet crucial concept because horizontal lines have a constant y-value and a slope of zero, indicating no rise over run.

Finding the y-intercept is a significant step when writing the equation of a line. The y-intercept represents the point where the line crosses the y-axis. This is the point where the x-coordinate is zero. In our exercise, we determine the y-intercept using the point provided: \((9, 5)\).Since our line passes through this point, we substitute these values into our simplified equation:\( y = b \).Substituting \( x = 9 \) and \( y = 5 \) into the equation gives us \( 5 = b \).So, the y-intercept \( b \) is 5. With this value, we can write the final equation of the line as \( y = 5 \).This means that wherever you go on this line, the y-value remains 5, regardless of the x-value. Understanding how to find the y-intercept helps you graph and comprehend the line's position better.